Papers

We prove two lower bounds for the first order oracle complexity of minimizing a $d$-dimensional $1$-Lipschitz convex function over the unit ball with $m$ bits of memory. We first show that any such (possibly randomized) algorithm must make $\tilde{\Omega}(\frac{d^2}{\sqrt{m}})$ oracle queries. For deterministic optimization algorithms, we show that $\tilde{\Omega}(\min\{d^{1.6},\frac{d^{8/3}}{m^{2/3}}\})$ queries are required. For all memory regimes of interest, these improves upon the previous best known lower bounds of $\tilde{\Omega}(\max\{\frac{d^{8/3}}{m^{4/3}},\frac{d^{4/3}}{m^{1/6}}\})$ and $\tilde{\Omega}(\frac{d^{5/3}}{m^{1/3}})$ for randomized and deterministic algorithms respectively. Notably, due to existing upper bounds, our lower bound for deterministic algorithms is the first to show a sharp oracle complexity phase transition around $m\approx d^2$, where a polylogarithmic change in memory leads to a $\mathsf{poly}(d)$ change in the number of required oracle calls. Further, when the suboptimality is polynomially small in $d$, our lower bound randomized algorithms is the first to show that $\tilde{\Omega}(d^2)$ memory is necessary to nearly match the optimal query complexity among algorithms without memory constraints. Previously, such a result was only known for the regime where the suboptimality is quasipolynomially small in $d$.

This paper explores the efficacy of quasi-Monte Carlo (QMC) weight initialization for meta-reinforcement learning within modern benchmark environments. Various sampling methods are used to bound a population-based search and aggregate an optimal prior from a baseline set of tasks. The QMC meta-priors show improvements in training convergence compared to modern orthogonal (SB3) defaults when extrapolated to similar unseen continuous control environments. In dissimilar tasks, the orthogonal orientation was globally superior for an unbiased search.

In this paper, a data-driven method for the computation of stabilizing state-feedbacks is proposed that leads to a rectified eigenstructure of switched linear systems. This means that all switching subsystems have the same sets of eigenvectors and the rectification allows to compute a common quadratic Lyapunov function ensuring asymptotic stability of the closed-loop system. The method is illustrated for two examples including a model of an aerosonde.

The unit commitment problem determines the optimal strategy to meet the electricity demand at minimum cost by committing power generation units at each point of time. Solving the unit commitment problem gives rise to a challenging optimization problem due to its combinatorial complexity and potentially long solution time requirements. Our proposed solution approach utilizes a decomposition method in conjunction with alternative models from the EGRET library. Results of this decomposition approach tested against four benchmarking systems show that significant computational speed ups are achieved.

We study online optimization for a broad class of structured non-convex non-smooth problems where each loss is a composition of a difference-of-convex function with a smooth mapping, and the feasible region is defined by constraint functions of the same kind. We propose a time-smoothed proximal linear algorithm and a local-regret measure based on a proximal residual mapping. We show that this residual is a proper stationarity measure for the original problem: its fixed-point condition implies first-order stationarity. Our analysis relies on a tangent-cone characterization for a feasible region described by composite difference-of-convex constraints, which is of independent interest and allows each update to be computed via a convex optimization oracle, despite the non-convexity of the problem. We establish a local-regret bound and a bound on the total number of inner convex subproblems. We also derive an error bound connecting the proximal residual to the distance to stationarity, providing a quantitative certificate of approximate stationarity.

We introduce RELTA-SGLD, a taming scheme that stabilizes superlinear stochastic-gradient updates while reducing unnecessary suppression of the original learning drift. A threshold determines where the taming turns on, while a relative-growth principle derived from the one-step Lyapunov stability condition determines the required taming strength. Together, they produce a lighter $\lambda$-scale denominator and preserve a nonvanishing far-tail return. As a consequence, we prove polynomial moment stability and first-order stationary accuracy in both $W_1$ and $W_2$ for nonconvex SGLD with superlinearly growing stochastic-gradient oracles, improving the corresponding half-order and quarter-order bounds for comparable stochastic-gradient tamed schemes. On Fashion-MNIST under active stabilization pressure, RELTA improves the mean learning metrics over both untamed SGLD and TUSLA and remains competitive with a tuned AdamW reference. In an ordinary-training regime, its lighter localized denominator reduces unnecessary perturbation of the original update and maintains nearly untamed learning dynamics.

Power grids, markets, and interacting populations, settle into feedback driven equilibria observed through unknown sensors. Our Equilibrium Causal Game (ECG) joins a game to its cyclic causal model, hidden inputs, sensor map, and rules for interventions and equilibrium selection; interventions edit declared objects and recompute equilibrium. Under stated conditions, ECG-separation is sound but incomplete in our examples. Back-door/half-trek routes identify observed queries. Yet for an untouched rotationally symmetric Gaussian block, second moments determine only a source-frame rotation, across which distinct-variable effects generically change. Unknown sensing creates a separate ambiguity. In passive stable linear models without self-effects, unknown wiring and full-rank unknown sensing leave $B$ completely unidentified for $d\ge2$. Under LiNG, non-Gaussianity removes the source rotation; mechanism interventions separate sensing from interactions. With unknown support, invariant sensing, aligned responses, and well-posed single-target interventions identify $(H,B)$ up to declared equivalence. Of $d$ targets, $d-1$ suffice exactly when the sole untargeted node directly parents all others; otherwise $d$ are needed. Acquisition probes are excluded; known wiring gives no universal count. With nonlinear sensing, isotropic Gaussian source blocks admit hidden twists within and across blocks in labelled environments preserving required radial laws. Conversely, under stated positivity, informative one-block changes, rank, and irreducibility conditions, the finest independent source-block representation is identified within the stated alternative class up to block permutation and blockwise coordinate changes, but not downstream mechanisms or the sensor/interaction split. Together, these results show which causal conclusions equilibrium data support and which require targeted experiments.

Bilinear systems with quadratic outputs (BQO) have recently emerged as an important system class, arising naturally in applications where both the dynamics and the quantities of interest depend nonlinearly on the state. Despite the growing interest in this class of systems, a systematic $\mathcal{H}_2$ framework for BQO systems has been lacking. In this paper, we develop such a framework by establishing an $\mathcal{H}_2$ inner product and norm for BQO systems, deriving output bounds in terms of the $\mathcal{H}_2$ norm, and obtaining first-order optimality conditions for $\mathcal{H}_2$ optimal model reduction. Building on these theoretical foundations, we propose an algorithm that computes a reduced BQO system satisfying these optimality conditions, and thus generalizing existing $\mathcal{H}_2$ optimal methods for bilinear and linear quadratic output systems. The effectiveness of the proposed framework is demonstrated on two numerical examples.

Controlling dynamical systems in real-time across multiple scenarios is critical to enabling adaptive control strategies, ensuring stability and efficiency. However, to tailor control actions in response to varying scenarios, traditional optimal control problems typically require several system simulations, which are often computationally demanding due to the high-dimensionality of the underlying spatio-temporal dynamics. In this work, we exploit SHallow REcurrent Decoder networks-based Reduced Order Modeling (SHRED-ROM) to synthesize a real-time closed-loop controller for high-dimensional and parametric dynamics, relying solely on limited state sensor readings. After training the model on a few optimal examples given by an expert demonstrator, SHRED-ROM mimics the expert behavior with effective distributed control actions in new scenarios, alleviating the curse of dimensionality. Moreover, a sensor forecaster is synthesized and used to close the loop at the latent level, thus efficiently mitigating possible sensor failures or delays. The performance of the proposed optimal control strategy is finally assessed on three challenging high-dimensional cases dealing with either parametric density control or fluid flow control.

Applying policy optimization to Model Predictive Control (MPC) yields high-performance and reliable controllers. However, the resulting controllers often overfit their training conditions and suffer significant performance degradation in unseen tasks. We propose a novel framework combining policy optimization with meta-learning to train highly adaptable MPC controllers. Our approach enables rapid adaptation to unseen tasks, maintaining high performance at a fraction of the computational cost required for full retraining. Furthermore, we integrate system identification into the pipeline to continuously refine both the MPC hyperparameters and the underlying predictive models. We validate our proposed methodology on a Ball-on-Plate system, demonstrating superior adaptability across various parameterized trajectory-tracking tasks.

We consider the design of optimal fixed-step first-order methods for $M$-Lipschitz convex optimization given $\|x_0-x_\star\|\leq D$. Prior works have identified several distinct fixed-step methods, parameterized by a matrix of stepsizes $W$, with the (information-theoretic) minimax optimal rate $MD/\sqrt{N+1}$ of objective gap convergence. We provide a complete characterization of every optimal fixed-step method. Moreover, we show every optimal fixed-step method can be derived from the constructive approach of~\cite{constructive_approach} and provide a polyhedral representation of the set of optimal methods through proof multipliers. From this characterization, we show that no anytime optimal fixed-step subgradient methods exist.

We study a proximal point type method for approximating solutions to equilibrium problems generated by pseudomonotone and strongly quasiconvex bifunctions over Hadamard manifolds, that is complete simply connected Riemannian manifolds of nonpositive sectional curvature. Next to the usual proximal step, the method we consider also incorporates an inertia step together with a subsequent over-relaxation, the latter of which is treated in the context of Hadamard manifolds, to our knowledge, for the first time. Making use of a quantitative approach towards such proximal methods for strongly quasiconvex optimization developed by the authors in previous work, we in particular provide effective arguments for the convergence of the method, yielding explicit, fast and very uniform rates of convergence for the distance of the iterates towards the solution. These results extend previous work by Grad, Lara and Marcavillaca on such a method over finite-dimensional Euclidean spaces for the first time to a nonlinear setting, with the quantitative estimates already being novel in the Euclidean case. In particular, our effective approach allows for a fine-grained view on the assumptions on the surrounding objects, so that we are able to either weaken or even fully discharge some previous assumptions.

We consider stabilisation of abstract boundary control systems and controlled partial differential equations with general unknown input disturbances and unmodeled nonlinearities at the input. We utilise the active disturbance rejection control approach to design a controller which rejects the input disturbance and achieves stability and external well-posedness of the closed-loop system for a class of boundary control systems with collocated inputs and outputs. We apply our main results to design controllers for one-dimensional wave and heat equations.

The rapid growth of the global aging population presents severe challenges to healthcare systems, necessitating efficient, equitable, and patient-centered care models. While Industrial Engineering and Operations Research (OR) provide robust optimization and decision-support tools to address these multidimensional complexities, current applications often remain fragmented. This paper presents a thematic review of 30 seminal studies at the intersection of OR and elderly care, categorizing the literature into home healthcare operations, polypharmacy management, and clinical chronotherapy. Our analysis highlights a significant methodological evolution from static, deterministic models toward dynamic and stochastic frameworks integrated with artificial intelligence (AI). Despite these advancements, a critical translational gap persists: the current OR literature is heavily dominated by process-level optimizations, such as staff routing, and struggles to translate these operational efficiencies into measurable clinical outcomes. Furthermore, holistic models bridging the transition between hospital and community care remain critically underexplored. To develop resilient and smart healthcare systems, this study proposes a conceptual framework that shifts the research focus from isolated operational tasks to integrated, multi-level decision-making. We emphasize the critical need for robust systems analysis, human-inclusive design, and the smartification of care through emerging digital technologies - including digital twins and large language models - to successfully bridge the gap between theoretical operational metrics and tangible patient-level health outcomes.

Distributed optimization offers significant advantages over centralized methods in terms of scalability and robustness when solving large-scale problems. In this paper, we propose a novel decentralized optimization algorithm that integrates Inexact Consensus ADMM (IC-ADMM) with a finite-time decentralized quantized communication algorithm. The proposed method enjoys three main benefits: (i) it operates on directed communication graphs, (ii) it requires only quantized local information instead of exact values, and (iii) it does not rely on solving the local subproblems exactly. Under the assumption that each node's local objective is strongly convex and L-smooth, the algorithm is guaranteed to achieve global linear convergence to a neighborhood of the optimal solution. Extensive numerical experiments demonstrate its advantages over existing methods in terms of convergence speed and communication efficiency.

In satellite design, it is common practice to add safety margins to the constraints to achieve conservative solutions that are robust to uncertainties. This robustness often comes at the expense of performance and it may be more appropriate to include uncertainties in the definition of the design problem. This work addresses such a challenge by applying techniques of multidisciplinary design optimization under uncertainty to an industrial use case. The latter is a pair of telecommunication satellites launched together in a stacked configuration. Each satellite is a strongly coupled multidisciplinary system while the two satellites are not coupled at all. This use case can be extended to an arbitrary number of satellites. By considering uncertainty quantification techniques such as sensitivity analysis and reliability-based design optimization, this study demonstrates that accounting for uncertainties in the design problem results in a 66% reduction in performance loss compared to the adding of a predefined safety margins, while guaranteeing the feasibility of constraints with high probability.

Motivated by sampling and approximation schemes arising in nonsmooth optimization, we study the stability of parameterized set-valued integrals under weak perturbations of the underlying probability distribution. For a compact parameter set, we show that compact convex-valued and jointly outer semicontinuous integrands induce set-valued integral maps that converge graphically in excess distance along any weakly convergent sequence of probability measures. The result holds under a superlinear integrability condition and provides a unified stability principle for measure approximations of set-valued expectations. We discuss the sharpness of the assumptions through examples. In particular, we emphasize that joint outer semicontinuity is required in general and that the superlinear envelope condition is tight relative to the classical i.i.d. empirical setting. As a consequence, we obtain outer stability of solution sets for stochastic generalized equations. We illustrate the stability result in several settings, including stochastic nonsmooth optimization with Markovian sampling, smoothing by mollifiers, and parameter-dependent distributional dynamics.

This paper presents a unified cost-modeling and optimization framework designed to evaluate hybrid discrete-variable/continuous-variable quantum key distribution (DV/CV-QKD) infrastructures operating within the SAFE (Secure and Efficient) long-term storage (LTSS) protocol. Our methodology jointly addresses the information-theoretic and computational dimensions of cryptographic durability over multi-decade horizons by coupling a quantitative risk model with a stochastic integer linear programming (ILP) formulation. Going beyond idealized physics-informed limits, the framework incorporates realistic next-generation industrial implementations and multiplexed coexistence specifications, together with a sample-average approximation (SAA) pipeline, to determine cost-optimal and structurally feasible SAFE topologies under transmission-budget and security constraints. The proposed framework is evaluated on both randomized synthetic deployments and realistic metropolitan-scale QKD infrastructures, including the Paris Metro-Scale and Greater Paris networks, to characterize the interplay between network topology, QKD modality, and deployment cost while enforcing a target global compromise tolerance $\epsilon$. Numerical results show that the economically optimal architecture is highly scenario-dependent and that both hybrid and homogeneous modality allocations naturally emerge from the optimization. More importantly, the analysis reveals a non-monotonic relationship between the minimum required QKD link capacity and the infrastructure cost: contrary to intuition, increasing the minimum required per-link secret-key rate may reduce the overall deployment cost by enabling a global transition toward more economical CV-based solutions, whereas further capacity increases do not necessarily yield additional savings.

The design of state observers for cyber-physical systems under sparse sensor biases, faults, or attacks has drawn substantial attention in recent years. While sparsity-based batch approaches, which collect multiple measurements and run offline, are relatively mature, online secure state estimation, for real-time state/attack recovery, is still an open problem. Although some algorithms have been proposed, convergence guarantees remain limited, even for the case of constant attacks. As a first step toward addressing this gap, we focus on constant attacks. We analyze the observability of this setting and we study several online sparse observers, derived from different methodological frameworks such as online sparse optimization and block Bregman methods. Some of the proposed observers are adaptations of existing algorithms to the secure state-estimation setting, while others constitute novel algorithmic contributions. The goal of this paper is to provide a unified overview of practically implementable, online sparse observers, discuss their convergence properties, and compare their performance through numerical experiments.

We develop a frugal primal-dual splitting with minimal lifting for solving structured monotone inclusions, involving cocoercive operators, linear compositions and parallel sums. This is established by defining hierarchical nodes and edges between them over a tree-structured graph, with arbitrary assignments of dual variables and cocoercive elements to primal nodes. This arbitrariness allows a great flexibility in terms of level-synchronous distributed computing, such as centralized or decentralized. The particular instances naturally extend the Douglas–Rachford splitting on various graphs, recover the parallel Chambolle–Pock, and solve a class of structured convex minimization problems. For the pure resolvent convex minimization subclass, we establish an O(1/k) ergodic rate for a restricted primal-dual gap over bounded test sets. Furthermore, we introduce a reformulation technique in a product Hilbert space to facilitate the convergence analysis, specifically to derive the o(1/k)-rate of asymptotic regularity

Distributed coordination of multi-agent systems frequently relies on cooperative protocols designed to achieve agreement on a prescribed, non-trivial trajectory. While the robustness of such protocols to various uncertainties is well documented, existing literature universally assumes that the target agreement trajectory itself remains invariant. This assumption may hold in ideal cases, but we prove that network perturbations can vastly modify the asymptotic agreement trajectory. We first investigate the exact trajectories of Linear Time-Invariant (LTI) agents subjected to dynamic coupling uncertainties by establishing a new Laplace-domain criterion that characterizes the specific closed-loop poles governing the perturbed agreement manifold. To formalize our analysis, we introduce the notion of structure-preserving dynamics, perturbations that maintain the null space of the communication graph's Laplacian, and contrast them with transmission only dynamics, affecting only the adjacency matrix. We prove a critical fragility within standard cooperative output regulation schemes: while static consensus is uniquely robust to heterogeneous transmission delays, synchronization to periodic trajectories is destroyed by arbitrarily small transmission delays. Furthermore, we demonstrate that for d-regular topologies, uniform transmission perturbations can easily shift the system to synchronize with an unexpected, entirely new frequency. These findings expose a previously unidentified vulnerability in classical robust synchronization, demonstrating that transmission dynamics necessitate fundamental structural modifications to networked reference generators.

This paper presents a comprehensive analysis of directional derivatives and error bounds for the merit function $\theta(x)=\sup_{a\in A}\bigl(-\Delta_C(F(x)-F(a))\bigr)$ associated with the vector optimization problem $\operatorname{Min}_C\{F(x):x\in A\}$, where $\Delta_C$ is the oriented distance function. We first prove that $\theta$ is concave and Lipschitz continuous on the whole space and derive its dual representation via the weak$^*$ compact convex set $K=\overline{\operatorname{co}}^{w^*}(S(C^+))$. At a weakly efficient solution $\bar x$, we obtain the explicit formula $\theta'(\bar x;d)=\min_{y^*\in W(\bar x)}\langle y^*,F(d)\rangle$ with $W(\bar{x})=\{y^*\in K:F^*y^*\in -N_A(\bar{x})\}$, characterize the zero-directional-derivative cone, and prove that, under a local error bound condition, the tangent cone to the solution set is $T_{E_w}(\bar x)=T_A(\bar x)\cap T_{\widehat A}(\bar x)=\{d\in T_A(\bar x):\theta'(\bar x;d)=0\}$. We establish the equivalence of thirteen distinct global error bound conditions, including characterizations via linear regularity, the global slope, an asymptotic condition, and perturbation stability. A central result shows that the global error bound property for $\theta$ on the feasible set $A$ is characterized by a uniform negativity condition on the unit-sphere minimal directional derivative, namely $\sup_{x \in A \setminus E_w} \varphi(x) < 0$. We also determine the optimal local error bound constant precisely as $1/\varphi(\bar x)$ when $\varphi(\bar x)>0$, and provide a counterexample demonstrating that an additional directional condition is essential when $\varphi(\bar x)=0$. These results provide a complete bridge between the directional derivative of the merit function and the geometry of the solution set, offering fundamental tools for the convergence analysis of algorithms in vector optimization.

Minimum-variance portfolios are well known to be highly sensitive to covariance estimation error. In this paper, we show that by imposing a block diagonal correlation structure, we can derive closed-form expressions for long-only minimum-variance portfolios that make this fragility explicit. These analytical solutions reveal that fragility is driven by threshold effects arising from the interaction between correlation structure and the assets' volatilities. Motivated by the latter insight, we propose robustification approaches that can be interpreted as structured shrinkage schemes that selectively attenuate unstable coupling while preserving the dominant risk structure. Unlike global shrinkage techniques, the proposed corrections are analytically grounded, require minimal tuning, and remain closely aligned with the minimum-variance solution. The framework extends naturally to general covariance matrices through clustering-based approximations. Empirical results on controlled simulations highlight a clear regime dependence. In homogeneous volatility settings, correlation-oblivious shrinkage achieves the best trade-off between risk and stability. In contrast, under heterogeneous volatility, correlation-aware shrinkage performs best by inducing sparsity and avoiding exposure to high-risk assets. Across regimes, the proposed methods consistently reduce out-of-sample variance and turnover relative to classical and clustering-based benchmarks, providing a principled and practical approach to robust portfolio construction.

For a graph $G$ and an integer $d \geq 0$, let $\chi^d(G)$ denote the $d$-defective chromatic number, and let $G \boxtimes K_{d+1}$ be the $(d+1)$-fold clique blowup of $G$. Norin and Steiner disproved the conjecture $\chi(G) = \chi^d(G \boxtimes K_{d+1})$ of Guo, Kang and Zwaneveld by exhibiting, for infinitely many $d$, graphs with $\chi(G) \geq (30/29) \chi^d(G \boxtimes K_{d+1})$, and they proved the universal upper bound $\chi(G) \leq 2 \chi^d(G \boxtimes K_{d+1})$. Writing $C_d = \sup_G \chi(G)/\chi^d(G \boxtimes K_{d+1})$ and $C^* = \sup_d C_d$, their results give $C^* \in [30/29, 2]$. We improve the lower bound: we exhibit an explicit 40-vertex graph $W$ with $\chi(W) = 11$ and $\chi^2(W \boxtimes K_3) = 10$, so that $C^* \geq C_2 \geq 11/10 > 30/29$, already at the smallest defect for which such a separation is possible, namely $d = 2$. All parameters are established by the proofs; the only computer-assisted input, the non-list-colourability of a certain 30-vertex, 10-colour list instance $(B,L)$, is certified by an independently checkable DRAT refutation.

Building on our previous general computational solution to Bellman's Lost-in-a-Forest Problem, we present a new approach and analytical formulas for the previously well-known escape path for the infinite unit-strip forest and unit broadworm by Zalgaller. Earlier studies addressed these problems exclusively through geometric methods. We reformulated the problem as an interval-cover problem and then formulated it as a constrained functional minimization problem. This constrained functional minimization can be directly discretized and subsequently solved as a convex optimization. Furthermore, we extend the analysis of various line segment. Finally, we show that, in the case of a closed escape path for the unit strip, the optimal solution is a curve of constant unit width.

This article develops a large-signal stability analysis for a sampled-data optimization-based secondary controller for distributed energy resources (DERs) in power systems. The induced closed loop combines nonlinear inverter power-flow dynamics, filtered active and reactive power measurements, constrained optimization updates, and interpolation-based actuation between sampling instants. We study this optimization-in-the-loop nonlinear sampled-data system beyond local linearization. The analysis provides computable bounds on the voltage, filtered reactive power, and the secondary control input. We further characterize steady-state operating points and establish how the optimizer objectives and constraints connect voltage regulation with equal per-unitized reactive power sharing. Finally, input-to-state stability of the frequency dynamics is established with respect to DER voltages and control inputs. These results provide a rigorous mathematical foundation for sampled-data optimization-based secondary control of DERs.

As electric vehicle (EV) adoption grows, quantifying the scheduling burden and economic cost of long-distance travel under the existing charging infrastructure becomes increasingly important for infrastructure planning and policy. This paper presents a scalable, optimization-based framework for scheduling EV charging stops along real-world charging stations and simulated long-distance personal vehicle trajectories across the United States using POLARIS. Taking the existing charging network as fixed input, the framework minimizes total detour and queuing costs for each vehicle while respecting plug capacity constraints at each station. The methodology proceeds in three phases: (i) infeasibility pruning via a forward-pass reachability heuristic, (ii) per-vehicle optimal charging schedule computation via dynamic programming on a directed acyclic graph, and (iii) capacity-aware iterative congestion resolution through a penalty-based heuristic that augments detour costs at congested stations, with a first-in, first-out queue fallback. Applied to approximately 2.7M origin–destination vehicle trajectories derived from a 1% sample of national personal travel demand within the POLARIS agent-based transportation simulation framework and covering 14,260 DC fast charging stations with 68,641 plugs from the Alternative Fuels Station Locator, the framework produces capacity-feasible schedules in under 1.3 hours on a 128-core high-performance computing cluster without requiring any commercial optimization solver. A three-tier economic analysis spanning operational costs, total cost of ownership, and amortized infrastructure investment is conducted to evaluate EV cost competitiveness relative to internal combustion engine vehicles across scenarios.

$\texttt{codesign-mcdp}$ is a Python library for formulating and solving $\textit{Monotone Co-Design Problems}$ (MCDPs) in the framework of Censi (2015). A design problem is a relation between two posets, a functionality poset $F$ and a resource poset $R$; given a target functionality, the problem asks for the antichain of minimal resources needed to deliver it. Design problems compose under three operators (series, parallel, feedback), and the resulting class is closed under composition. The library implements the antichain calculus, six primitive design-problem types, the three composition operators, a Kleene fixed-point solver, and two high-level builders (an MCDPL-style declarative builder and a modular $\texttt{System}$ builder). Further layers add set-based and stochastic uncertainty, compositional online learning, and temporal, vector-state, and online co-design, alongside a suite of worked examples.

In this work, we study small-noise asymptotics of risk-sensitive exit-time control problems governed by stochastic differential equations with path-dependent coefficients. Our main result establishes the convergence of the $\log$-transformed exit-time problem to a deterministic control problem with path-dependent coefficients. For its proof, we first derive a novel variational representation for general $\log$-transformed stochastic control problems with path-dependent coefficients, combining tools from the theory of path-dependent partial differential equations and convex expectations on path spaces. In a second step, we use probabilistic methods to analyze the convergence of the resulting variational formulas. To illustrate the scope of our analysis, we consider a computable example for a stochastic differential equation with memory and characterize the limiting problem and associated control strategies.

We study the small-regularization limit for $L^p$-regularized optimal transport with $1<p<\infty$ and for entropically regularized optimal transport (EOT). The exact first-order (respectively, second-order) asymptotics are determined explicitly under mild assumptions on the source and target measures. Our work generalizes the existing results for quadratic and entropic regularization, and connects them by a natural interpolation via $p\in(1,2)$. We derive all these asymptotics in a unified manner by a novel approach that separates the local computation of the optimal profile from the global enforcement of the marginal constraints: convex duality leads to Gaussian profiles for entropy and Barenblatt profiles for $L^p$-regularization, while a quantization construction turns these local profiles into couplings.