Papers

Autonomous small-body proximity operations require continuous-thrust guidance under uncertain gravity, solar-radiation pressure (SRP), and stochastic disturbances. We combine iterative covariance steering (iCS) with $L_1$ distributionally robust adaptive control ($L_1$-DRAC) to provide risk-aware collision avoidance despite mismatch between the nominal planning model and the true dynamics. Iterative covariance steering plans a nominal feedback policy satisfying distributionally robust conditional value-at-risk keep-out constraints, while $L_1$-DRAC compensates for dynamics uncertainty and bounds the residual distributional mismatch through a Wasserstein radius used by the planner. In $\mathbf{1000}$ paired Monte Carlo trials with gravity, SRP, and diffusion mismatch, $L_1$-DRAC adaptive control reduces the keep-out violation rate from $\mathbf{32.7\%}$ to $\mathbf{0.2\%}$ and the physical collision rate from $\mathbf{16.4\%}$ to zero, without actuator saturation.

We develop a neural transport framework for nonlinear, nonlocal aggregationdiffusion equations arising in chemotaxis, polymer dynamics, and related applications. Based on the Onsager variational principle, we reformulate the governing equation as a constrained optimal control problem, taking the velocity field as the control and evolving the density via the associated continuity equation. The velocity field is parameterized by a neural network trained on the variational objective evaluated along particle trajectories. By coupling the density and generalized score equations into a single system solved via the Euler method, the score function propagates efficiently for loss evaluation. Furthermore, we establish a rigorous error analysis that decomposes the total error into approximation, optimization, Monte Carlo sampling, and time-discretization components, and prove corresponding error bounds. Numerical experiments across several representative models demonstrate the accuracy and effectiveness of the proposed approach.

Parents seeking childcare often face long waitlists. At the same time, vacancies at childcare centers can remain unfilled for extended periods. We trace this paradox to two persistent features of childcare services. First, families consider multiple child care options due to enrollment uncertainties, resulting in phantom listings that remain on waitlists even after families have found care elsewhere or no longer need a slot. Second, filling a slot is time-consuming: centers learn whether a family is actively seeking enrollment only after making an offer and waiting for a response. As families pursue alternatives while they wait and their children age, these delays and feedback effects amplify the mismatch between demand and available capacity. We study two operational remedies. First, we examine regular verification that removes phantom listings before offers are made, improving the efficiency of enrollment and reducing vacancies. Second, we study mixed-age classrooms, in which some slots designated for older children can be flexibly used by younger children. This flexibility increases utilization, shortens waits, and reduces wasted offers. Its benefits extend beyond conventional pooling: as children move between age groups, classrooms can be filled through internal flows rather than costly external search, further reducing enrollment delays. Together, verification and mixed use offer a way to expand effective capacity in early childhood classrooms, where regulatory and operational constraints make adding physical capacity particularly costly.

Stochastic dual dynamic programming (SDDP) and its variants are run in practice with forward passes that sample the noise at random. Recent iteration-complexity results favour another choice: when the trial points are selected deterministically, for instance along the scenario with the largest gap, the number of iterations is polynomial in the horizon $T$, whereas every bound we know of for randomly sampled forward passes is exponential in $T$. We show that this is not intrinsic to random sampling, for a broad class of trajectory-following dynamic programming algorithms, which includes SDDP, stochastic dual dynamic integer programming and stochastic Lipschitz dynamic programming. With random sampling, and with Lipschitz constants, diameters and per-stage loss ranges bounded independently of the stage and of the horizon, the expected number of iterations whose policy is not $T\varepsilon$-optimal is $O(T\varepsilon^{-(d+1)})$, where $d$ is the state dimension: linear in $T$, as for deterministic selection rules. The proof needs no particular scenario to be sampled: the gap between the expected cost of the current policy and the current lower bound equals the expected sum of one-step Bellman residuals along the sampled path, and Lipschitz cuts that are tight at the visited states turn the positive residuals into permanent increases of a bounded potential. The results extend to noise without finite support, to backward passes on a sample average approximation, and to stationary and periodic infinite-horizon SDDP with geometric pass lengths.

This paper studies an open network design problem of constructing graph topologies with maximum algebraic connectivity under fixed numbers of vertices and edges. A density-dependent approach is proposed that decomposes the design task into two stages: a high-quality, low-cost structural backbone construction and a reinforcement learning completion stage. The method selects the backbone based on density, using complete multipartite graphs in dense regimes and Cayley graphs in low-to-intermediate regimes, and then refines the remaining edges through a learning-based procedure. Numerical results show that the proposed method achieves high algebraic connectivity with favorable runtime scalability, outperforming existing methods. These results support a structural-family-first strategy for scalable network design.

The so-called “100% rule” is a somewhat classical and yet somehow obscure rule that gives some local sensitivity-analysis information based on the very limited local sensitivity-analysis information that is often made available by linear-programming software, derived from an optimal basis that is hidden from the user. Introduced in a classic undergraduate textbook in 1977, half a century ago, it was only picked up on by researchers in a very limited way, and while it appears in some undergraduate textbooks, it tends not to appear in most modern graduate-level textbooks. Our contributions are to celebrate and revive interest in the 100% rule and to extend it in a meaningful way. We introduce a cone rule that certifies primal feasibility for more right-hand sides than the 100% rule does, using the same information, and that can be applied in linear time. We then study when this cone rule is tight, that is, when it captures the entire cone of right-hand sides for which the basis remains feasible. We characterize tightness in every dimension for right-hand sides interior to that cone, make the characterization explicit for m=2 and m=3, and settle the question for tridiagonal bases in every dimension: tightness is impossible once m>=4, and for m=3 we give an explicit criterion in the entries of the basis. We give further results for symmetric, integer and unimodular bases. Finally, when tightness fails, we measure the fraction of the feasibility cone captured by the rule using normalized solid angles. For the autoregressive family at m=3, we obtain a closed-form candidate for the infimum of this fraction over all right-hand sides, whose optimality is supported numerically. We also obtain a closed-form expression for the best case over most of the correlation range, subject to two numerically verified properties, and estimate the best-case value numerically more generally.

We study multiblock convex–concave saddle-point problems of the form $\min_x\max_y\{f(x)+H(x,y)-g(y)\}$, with separately charged partial-gradient oracles for all three objective components. We impose joint smoothness and strong convexity bounds on the functions $f$ and $g$, together with blockwise Lipschitz conditions on the partial gradients of $H$, so that the resulting oracle complexities reflect the smoothness and dependency parameters specific to each oracle. Under strong convexity, we develop a randomized lifted extragradient method that achieves linear convergence while providing simultaneous complexity guarantees for all oracles. The partial-gradient complexities for $f$ and $g$ exhibit the expected square-root dependence on the corresponding block condition numbers, whereas the coupling-gradient complexities depend on the associated curvature-normalized smoothness parameters. Finite-dimensional bilinear subclasses provide lower-complexity benchmarks within a randomized blockwise linear-span model. When strong convexity of $f$ and $g$ is not assumed, a regularization argument yields expected restricted-gap guarantees with accuracy dependence $\varepsilon^{-1/2}$ for the objective-gradient oracles and $\varepsilon^{-1}$ for the coupling-gradient oracles, up to logarithmic factors. Experiments show observed oracle savings and runtime improvements in regimes of poor objective conditioning.

We study how interpolation affects local steps and parallel sampling in monotone variational inequalities (VIs), with $m$ workers, $K$ oracle calls per worker per round, and $N$ rounds. Under the strong growth condition (SGC), we determine the minimax rate for affine VIs, attained by local extragradient with worker averaging. For nonlinear monotone VIs and convex-concave saddle problems with Lipschitz operators satisfying SGC, we improve the stochastic terms of bounded-variance expected-gap guarantees from $(KN)^{-1/2}$ to $(KN)^{-1}$ with local steps and from $(mKN)^{-1/2}$ to $(mKN)^{-1}$ with minibatches. Under strong monotonicity, we improve the noise-dependent condition-number scaling of existing extragradient bounds from quadratic to linear. The resulting monotone-gap and strongly monotone accuracy bounds match lower bounds up to logarithmic factors in $m$. Under generalized smoothness and SGC, adaptive steps give polynomial dependence on the initial radius. For affine VIs with globally bounded oracle variance, we also attain the minimax rate: the deterministic rate over $KN$ sequential calls plus the statistical rate over all $mKN$ samples. For composite VIs with smooth convex sample interpolation and an exactly evaluated monotone Lipschitz component, accelerated mirror-prox sliding achieves an $N^{-2}$ gradient term, a $(KN)^{-1}$ monotone term, and a $(mKN)^{-1}$ sampling term, without assuming SGC.

Large language models (LLMs) are increasingly being explored to automate operations research modeling, reduce modeling time and lower the expertise barrier to optimization based decision support. However, this process often introduces inconsistencies between generated artifacts and the original problem, which we refer to as optimization modeling hallucinations. Despite progress in general-purpose hallucination mitigation, optimization modeling poses a distinct repair challenge: restoring fidelity to the original problem through coordinated model-code updates. We introduce OPT-Kraken, a training-free hallucination repair framework. To the best of our knowledge, it is the first post-hoc framework for repairing hallucinations in LLM-based optimization modeling artifacts. It extracts problem requirements and instance data, localizes errors by checking problem-model fidelity, model-code consistency, and data grounding, and selects repair granularity by the affected scope. For local repair, category rules and instance evidence are compiled into contracts specifying permitted edits, expected effects, and protected content. Experiments on established optimization modeling benchmarks show positive gains across automatic modeling frameworks and fine-tuned models. On zero-shot artifacts from multiple base models, OPT-Kraken effectively repairs optimization modeling hallucinations while preserving initially correct artifacts. These results demonstrate effective and controlled repair for LLM-based optimization modeling artifacts.

Parameter convergence in recursive identification requires persistent excitation, which is typically enforced with a probing signal that degrades performance if retained indefinitely. Regulating the probing amplitude with the one-step prediction error is insufficient, since a small prediction error does not imply parameter convergence. This paper proposes a self-regulating excitation law that scales the probing amplitude with the associated covariance matrix, so that the excitation vanishes only as fast as the estimator's own measure of remaining parameter uncertainty allows. The key idea is that the excitation amplitude must decay more slowly than the covariance measure, the largest eigenvalue of the covariance matrix in this work, for parameter convergence to be preserved. Under the proposed excitation law, the excitation amplitude and the covariance measure are shown to jointly converge to zero while the parameter estimate converges to the true parameter, with the excitation vanishing more slowly than the covariance measure throughout. A scalar exponent in the law trades the rate of covariance decay against the amount of excitation retained. Numerical results confirm both properties.

This paper integrates reference governance with Dynamic Mode Adaptive Control (DMAC) to enforce constraints without a prior plant model. DMAC identifies and updates a discrete-time model online from measured state and input data, and the reference governor (RG) uses this identified model, rather than the true plant dynamics, to predict constrained closed-loop behavior. Because the prediction model changes as DMAC adapts, a governed reference that was previously feasible may become infeasible, and the classical interpolation-based RG may be unable to move the reference in the direction required to recover predicted constraint satisfaction. The proposed DMAC-RG framework instead searches directly over the governed reference rather than over an interpolation factor. When feasible references exist, the governed reference is selected to track the desired command, with an optional penalty on deviation from the previously applied reference. When the finite-horizon feasible set is empty, the reference is selected to minimize predicted constraint violation while retaining the same tracking preference. This work is a numerical investigation and does not provide theoretical guarantees of recursive feasibility, constraint satisfaction, or closed- loop stability. Numerical examples on a linear system, a nonlinear Van der Pol oscillator, and a high-dimensional Burgers equation under partial-state measurement demonstrate that the proposed RG enforces constraints using only the model identified online by DMAC, without access to the true plant dynamics or the complete system state.

We consider stochastic nonsmooth nonconvex composite optimization, which includes several important problems such as constrained optimization and the regularized training of neural networks. The objective is the sum of a possibly nonsmooth nonconvex Lipschitz function and a convex regularizer, and the function is accessed through stochastic gradients or function values. The goal is to find a point that satisfies a Goldstein-type stationarity condition designed for composite objectives. To our knowledge, no oracle complexity bound for this setting is known under first-order access, and existing complexities under zeroth-order access are suboptimal. To handle this issue, we employ the framework of online-to-nonconvex conversion, which chooses update directions by an online learner and is known to achieve optimal rates for noncomposite problems. We extend the framework to our composite scenario by introducing new losses for the learner, which contain the regularizer itself rather than its linearization and for which a variant of online mirror descent achieves low regret. We show that the resulting algorithm finds such a point with $O(\delta^{-1}\varepsilon^{-3})$ stochastic gradient queries or $O(d\delta^{-1}\varepsilon^{-3})$ function-value queries, where $\delta$ is the Goldstein radius, $\varepsilon$ is the stationarity tolerance, and $d$ is the dimension. These rates match the optimal ones for noncomposite nonsmooth nonconvex optimization, demonstrating that the additional convex regularizer does not worsen the oracle complexity. We also give rates for the smooth case and present numerical experiments.

The discrete-time control barrier function condition for a safe set that is a union of convex sets is nonconvex in the control input. For safe sets defined by a matrix concave function through the number of its nonnegative eigenvalues, this paper shows that the set is a union of convex sets, and that the nonconvexity arises because at least one member of the union must hold, not every member. Selecting eigenvectors of the matrix function at the current state yields a convex input constraint that acts only on the eigenvalues determining membership in the set. This constraint is implied by the matrix-wide condition of prior work, and it guarantees a geometric lower bound on each of those eigenvalues along closed-loop trajectories. A double-integrator simulation with a polytope obstacle and a spectrahedron obstacle compares the proposed filter with the matrix-wide condition.

Trapped-ion quantum simulators are powerful platforms for exploring many-body physics, yet engineering of arbitrary interaction graphs remains a central challenge. To leverage the intrinsic structure of native motional modes and thereby enhance programmability, a residual-guided optimization protocol is introduced for the systematic design of multi-tone global drive spectra. While the achievable interaction fidelity is fundamentally bounded by the available motional modes, this adaptive strategy converges on the theoretical limit using a number of laser tones that scales nearly linearly with system size. The versatility of this method enables the synthesis of both long-range and traditionally difficult short-range coupling topologies. Additionally, by incorporating a penalty for residual motional excitation, the algorithm effectively mitigates errors associated with incomplete closure of phase-space trajectories. Overall, this scalable framework significantly expands the programmable capabilities of trapped-ion architectures while maintaining low computational overhead and high potential for experimental implementation.

The paper considers a system of unidirectional first-order hyperbolic partial differential equations (PDEs) coupled with ordinary differential equations (ODEs), modeling two-phase advective transport processes subject to both boundary and distributed input delays. To address the system defined over two spatial domains, we design a set of three backstepping transformations involving both Volterra- and Fredholm-type integral operators, which introduce eight kernel functions: five associated with the PDE states and three with the ODE states. Since the distributed delayed variable spans the two spatial domains, its transformation must integrate over all state variables, leading to three-dimensional kernel functions with singular initial conditions involving Dirac delta functions that serve as sampling operators to establish mappings between variables of different dimensions. By employing the method of characteristics and successive approximations, we prove the well-posedness of the kernel equations. On this basis, we prove the invertibility of the Fredholm transformation and establish the exponential stability of the closed-loop system in the $L^{\infty}$ norm under the delay-compensated controller. Simulation results for a linear example and a nonlinear screw extrusion model are presented to demonstrate the effectiveness of the proposed method.

We establish matching lower bounds for deterministic first-order optimization of globally Lipschitz geodesically convex functions on hyperbolic space. A global minimizer lies within distance $r$ of a known point, each query returns an exact function value and a selected Riemannian subgradient, and the target objective gap is $\varepsilon Lr$, where $L$ is the Lipschitz constant. For sectional curvature $-k^2<0$, let $\rho=kr$ and $\zeta=\rho/\tanh\rho$. The optimal worst-case query complexity $Q^\star$, taken uniformly over dimensions, satisfies $Q^\star(\rho,\varepsilon)=\Theta(\zeta\varepsilon^{-2})$ for every $\rho>0$ and $0<\varepsilon\le1/64$. The new lower bound covers arbitrary adaptive deterministic queries and arbitrary outputs, matching the projected-subgradient upper rate of Zhang and Sra (2016). It removes the geodesic-span and historical-halfspace restrictions of earlier matching lower bounds. The construction extends a radial source from a convex carrier with boundary. A small residual cut selects minimizer candidates while an exact hyperbolic persistence inequality keeps every historical contact valid under future carrier growth. One fixed globally convex objective and one fixed subgradient selection consequently realize all exact replies simultaneously. Each query consumes $O(\varepsilon^2)$ of a geometric potential whose available budget is $\Theta(\zeta)$, yielding the product lower bound in a dimension linear in the query horizon.

The Simplex method is among the most widely used approaches for solving linear programs. Starting at a vertex solution of the feasible region, the algorithm proceeds through a sequence of basis exchanges (known as pivots), each corresponding to a move along an improving edge of the polyhedron toward a better vertex. A central challenge affecting the efficiency of the Simplex method is degeneracy, which can cause long sequences of pivot operations that fail to change the current vertex solution. In this paper, we prove the existence of a pivot rule which is able to escape degeneracy and follow any given shadow edge-direction when initialized at some compatible basis, with a linear number of degenerate Simplex pivots. As a byproduct of our result, we obtain an improved bound on the number of degenerate Simplex pivots needed to solve linear programs defined on 0/1 polytopes.

This work is concerned with a stabilizing adaptive dynamic programming (ADP) approach to approximate solution of a given infinite-horizon optimal control problem. Since the latter problem cannot, in general, be solved exactly, a parametrized function approximator for the infinite-horizon cost function is introduced in ADP (so called “critic”). This critic is used to adapt the parameters of the function approximator. The so called “actor” in turn derives the optimal input of the system. It is a notoriously hard problem to guarantee closed-loop stability of ADP due to the use of approximation structures in the control scheme. Since at least stabilizability is always assumed in the analyses of ADP, it is justified to invoke a respective Lyapunov function. The proposed ADP scheme explicitly uses the said Lyapunov function to simultaneously optimize the critic and guarantee closed-loop stability. A Hessian-free optimization routine is utilized for the actor and critic optimization problems. Convergence to prescribed vicinities of the optima is shown. A computational study showed significant performance improvement for the critic-based approach compared a nominal stabilizing controller for a range of initial conditions.

Multiple candidate flight paths between the same vertiports provide flexibility for managing noise exposure and cruise separation in on-demand urban air mobility (UAM). This paper introduces the fleet scheduling problem with alternative flight paths (FSP-AFP). We develop a time-expanded fleet-flow formulation for a finite aircraft fleet, in which each service or empty repositioning flight is assigned a planar path from a predefined set of alternatives connecting its origin and destination vertiports. These path choices are jointly optimized with cruise altitudes, departure times, and repositioning movements, while maintaining aircraft flow balance and enforcing geometric separation between flights cruising concurrently at the same altitude. The objective combines flight costs, service departure delays, and population-weighted noise exposure. A tailored branch-and-cut algorithm incorporates three complementary clique constructions based on a request-augmented conflict graph, exploiting physical flight conflicts, request exclusivity, and request-route relationships. Computational experiments show that, compared with a baseline implemented using Gurobi's native lazy-constraint functionality, the proposed algorithm generally obtains stronger lower bounds and finds feasible solutions for all test instances, while generating fewer cuts on average and achieving a 43.16-fold reduction in the mean number of processed search nodes. An operational case study shows that increasing the number of candidate planar routes per vertiport pair from one to four reduces the weighted objective by 6.71% and modeled noise exposure by 15.14% under the cruise-separation constraints. Further increases in the number of candidate routes yield only marginal improvement in the objective value. These findings show the value of coordinating alternative flight paths, scheduling, and fleet circulation in UAM.

We study the exact controllability of the cubic nonlinear Schrödinger equation in the exterior $\Omega=\mathbb{R}^n\setminus\Theta$ of a non-trapping obstacle $\Theta$, with internal controls supported outside a large ball, and the corresponding boundary control problem on $\Omega_0=B_{R_0}\setminus\Theta$ with Dirichlet controls acting only on the outer sphere $\partial B_{R_0}$. Using the local smoothing effect of Burq, Gérard and Tzvetkov [9], we prove observability inequalities for the linear Schrödinger equation in the whole scale of Sobolev spaces $H^\sigma_D(\Omega)$, $\sigma\in[-2,2]$, associated with the Dirichlet Laplacian; they require only the non-trapping assumption (no star-shapedness of $\Theta$), and their proofs use no normal boundary traces. Combined with Strichartz-type estimates and a perturbation argument, this yields local exact controllability in $H^1_0(\Omega)$ and in $H^2(\Omega)\cap H^1_0(\Omega)$, in dimensions two and three, around the zero solution and, for internal controls and under a unique continuation assumption, around nontrivial trajectories. The same method applies to the quintic equation, which is energy-critical in dimension three. Several open problems are discussed.

This paper considers a nonconvex fractional optimization problem with composite structure and nonlinear equality constraints. We reformulate the problem as a non-fractional min-max problem with corresponding optimal solutions. By linearizing the nonlinear constraint terms in the augmented Lagrangian and incorporating Bregman proximal linearization and a relaxation factor in $(0, 2)$ into the alternating direction method of multipliers (ADMM), we develop a Bregman proximal linearized ADMM with guaranteed subsequential convergence to a lifted critical point. Convergence of the entire sequence is established under the Kurdyka–Łojasiewicz (KL) property. We further derive convergence rates under either a Hölderian value proximity error bound condition or the KL property, with the corresponding exponent in $[0, 1)$. In particular, we establish superlinear convergence for exponents in $(0, 1/2)$, together with finite, linear, and sublinear convergence in the remaining cases. Numerical experiments demonstrate the effectiveness of the proposed algorithm.

Finding the extension complexity (xc) of a polytope is equivalent to finding the non-negative rank of its slack matrix. We provide a formulation for the rectangle and refined rectangle covering, bounding the non-negative rank of diverse non-negative matrices. While the bounds are known, our formulation enables us to use boolean satisfiability (SAT) solvers, which proves to be a strong tool. We obtain improved values for lower bounds on the non-negative rank of multiple matrices. In particular, we determined the xc of some regular polygons.

Expectiles are the only law-invariant risk measures that are both coherent and elicitable. Unlike Conditional Value-at-Risk (CVaR), however, they do not admit a Rockafellar–Uryasev representation that admits tractable Wasserstein reformulations. We address this difficulty by developing an envelope theorem for worst-case expectiles that characterizes the worst-case expectile over a Wasserstein ambiguity set as the unique root of a worst-case expectation with a two-piece affine integrand. This representation permits direct application of standard Wasserstein duality. Using this result, we reformulate a multi-period tri-level mean–expectile portfolio problem as four parametric linear programs with constraints. We establish four structural properties of the proposed model: an endogenously damped price of robustness, a decision-dependent critical radius beyond which the expectile tail component becomes inactive, exact recovery of the nominal model at zero ambiguity, and a characterization of how the Wasserstein ground metric determines whether the limiting portfolio becomes more concentrated or more diversified. Numerical experiments on 90 FTSE constituents over 3,341 out-of-sample trading days show that the expectile model outperforms a CVaR model matched on ambiguity set, radius, ground metric, and trade-off weight in all nine parameter cells—significantly so whenever the radius is non-trivial. The experiments further confirm the predicted degeneracy under the ground metric.

The computation of the vertices of a polyhedron described by a system of linear inequalities is a central problem in polyhedral computation. It is a fundamental step in the conversion between H-representations, by linear inequalities, and V-representations, by vertices and extreme rays. This operation plays an important role both in the study of polyhedra and their combinatorics in mathematics and in applications to software and system verification. We present a certificate-based approach for formally verifying the computation of the vertices of a polyhedron. Given an informally computed list of vertices, our method allows to certify in the proof assistant Rocq that the list is complete, or even exact. The cornerstone of the method is a new completeness criterion based on an abstract simplicial complex that generalizes a triangulation of the normal fan of the polyhedron. A significant advantage over previous approaches is that the usually expensive numerical computations are essentially reduced to membership tests to the polyhedron, while the other steps are cheap combinatorial tests. We implement the certification method and prove its correctness in the proof assistant Rocq. We experiment with it on a variety of polyhedra, including Birkhoff polytopes, cross-polytopes, cubes, permutahedra, hypersimplices, and high-dimensional polytopes involved in the disproof of the Hirsch conjecture. Our experiments show that certification with the Rocq-to-OCaml extracted checker is typically 1.5x to over 5x faster than vertex enumeration by the state-of-the-art informal C implementation lrslib of the reverse search method.

We consider the problem of learning linear dynamical systems under adversarial contamination from a single trajectory of length $T$. While identification of linear dynamical systems itself is well-studied, the problem of robust system identification under adversarial contamination is relatively less explored. In this work, we study the setting where a fraction of the $T$ observations are contaminated by adversarial outliers. We propose different estimators based on relaxations of least-trimmed squares along with an alternating minimization algorithm. Furthermore, we also propose two estimators which exploit the group-sparsity (through penalization/hard-constraints) of the outliers. For the estimator with group-sparse penalty, we derive non-asymptotic error bounds which establish its robustness to outliers. We also show empirically that the proposed estimators work well in practice.

This paper considers the reach-stabilize prob- lem for a class of nonlinear control-affine systems with unknown parametric uncertainties, where the system states must remain in a safe set at all times, or enter a safe set in finite time and then remain in it, and converge to a goal point. An estimator is designed that generates a parameter estimate and a computable, nonincreasing bound on the estimation error from a known initial error bound, without requiring persistence of excitation. The bound defines margins that are added to a control barrier and a control Lyapunov function condition, which are then enforced in a quadratic program for efficient control design. It is shown that, for the closed-loop system, the safe set is forward invariant when the system starts within the safe set and is finite-time reachable from outside the safe set with a recovery-time bound that does not depend on the unknown parameter, and that the goal point is exponentially stable. In two numerical examples, with the initial state outside and inside the safe set, the proposed control policy, a baseline oracle control policy that uses the true parameter, both recover or remain in the safe set and converge to the goal point, while another baseline control policy that uses a fixed, incorrect, parameter does not remain

We consider the problem of learning structured linear dynamical systems over convex sets $\mathcal{K}$, where only a small subset of the observations are available at each time point. An estimator which minimizes a bias-corrected, potentially non-convex objective function is proposed. Non-asymptotic bounds are obtained for the statistical error, which depend on the local complexity of $\mathcal{K}$, the trajectory length $T$, and the sub-sampling probability $p$. Convergence of the projected gradient descent algorithm is also established. The general theory is applied to settings where (i) $\mathcal{K}$ is a subspace, (ii) $\mathcal{K}$ is the set of bi-isotonic matrices, and (iii) $\mathcal{K}$ is the set of matrices whose rows are formed by sampling Lipschitz functions. We show meaningful recovery of the transition matrix is possible for values of $T$ much smaller than what is required in the unconstrained case, and for $p = o(1)$.

Near-term quantum approaches to combinatorial optimization are limited by qubit counts, circuit fidelity, sampling cost, and the difficulty of encoding constraints, while machine learning is increasingly used to configure and control quantum optimization workflows. We call such workflows adaptive: decisions conventionally fixed in advance, from formulation and penalties to shot budgets, backends, and whether to invoke a quantum processor at all, are made by learned policies that respond to the instance, the progress of the solve, or the hardware. This review examines three paradigms, AI for quantum optimization, quantum for AI-driven optimization, and AI-quantum co-optimization, and organizes the literature by the decision being learned rather than by application. A structured search identified a 119-paper corpus, of which 67 papers form an evidence core coded in detail. The evidence is considerably stronger for AI-assisted quantum optimization than for the reverse direction: learning already reduces quantum evaluations, improves initialization, supports decomposition and penalty control, and mitigates noise, whereas evidence that quantum computation improves learned optimizers remains largely confined to small-scale simulation. Experimental controls are thin: of 52 studies in the three paradigms, 22 include no classical baseline, the quantum contribution is fully isolated in 10 of 24 where an ablation applies, and the median largest experiment uses 16 qubits. We introduce an M0-M5 evidence hierarchy, from simulation to practical quantum advantage, and find no broadly convincing result at the highest level. We argue that scaling is increasingly a systems problem: the question is not only whether a problem fits on a quantum processor, but how classical and quantum resources should be allocated across the optimization process.

Standard weight decay treats each weight matrix as a vector and ignores its spectral structure. We introduce spectral weight decay, a post-step decoupled nuclear-norm update that applies additive rather than multiplicative spectral shrinkage. We connect the update to approximate proximal descent and show that its sensitivity to update order can exceed that of conventional $\ell_2$ weight decay near rank deficiency. Across LLaMA models with $124$M to $500$M parameters, spectral weight decay lowers effective rank and improves SVD-LLM compression at matched validation loss. At $500$M and a $4\%$ distortion budget, it reaches $1.89\times$ compression and $1.18\times$ GPU inference speedup, compared with $1.14\times$ and $1.01\times$ after standard weight decay. Under fixed-horizon training with $60\%$ label noise, it also improves final mean clean-test accuracy over matched $\ell_2$ regularization by up to $17.8$ points on MNIST and $4.6$ points across four BERT-base tasks. Code is available at https://github.com/brain-lab-research/SpectralWD.

Computing local Stackelberg equilibria in nonlinear sequential games is challenging because gradient-based best-response methods may diverge, cycle, or converge to stationary points that do not satisfy the required equilibrium conditions. These failures can result from curvature asymmetry, unstable response mappings, and lack of invariance with respect to the follower's best-response manifold. This paper introduces the Stackelberg Sliding-Mode Algorithm (SSMA), a control-theoretic framework that recasts Stackelberg equilibrium computation as a manifold-stabilization problem. The follower and leader first-order optimality conditions define Stackelberg sliding manifolds, and sliding-mode dynamics drive the iterates to these manifolds in finite time. The follower curvature and leader reduced-curvature conditions determine manifold attractivity, making valid local Stackelberg equilibria attractive while rejecting stationary points that fail the second-order equilibrium conditions. The resulting approach integrates finite-time manifold stabilization, Stackelberg-consistent dynamics, and curvature-based equilibrium selection within a unified framework. Across 500 nonconvex Monte Carlo trials, SSMA achieved 100% success, reached the prescribed tolerance in a median of 26 iterations, compared with 456 for the nearest fully successful baselines, and attained terminal residuals near \(10^{-16}\), while converging to a valid local Stackelberg equilibrium.