Papers

This paper extends prior work on linguistic pattern based facility layout optimization by enhancing the LP Alinks framework with an explicit spatial uniformity criterion. While earlier studies demonstrated that linguistic patterns can effectively encode expert knowledge and guide agent based layout emergence, their optimization scope remained limited to cost oriented objectives. To address this gap, we introduce the Normalized Coverage Score (NCS), a scale adjusted measure of spatial evenness that complements the classical flow distance economic objective and enables systematic exploration of cost uniformity trade offs. A full factorial experiment comprising 324 conditions evaluates the combined effects of problem size, link density, virtual force scaling, and two families of membership functions on both objectives. Five way and nested three way ANOVAs reveal that structural factors (number of objects and link density) exert a dominant baseline influence on both economic performance and spatial uniformity. However, while economic cost is overwhelmingly governed by these structural characteristics, uniformity is substantially more sensitive to the linguistic pattern parameters, which control the dispersion compaction dynamics of the emerging layouts within the structural constraints. Based on these interactions, we derive a parameter-selection matrix that prescribes settings for cost minimization, uniformity maximization, or balanced compromise. Comparative analyses with Drezner's method, MDS, and non metric MDS demonstrate that the extended LP Alinks framework consistently attains superior uniformity while maintaining competitive economic performance, making it a robust and interpretable decision support tool for early stage facility layout design.

In this paper, we propose and study a class of differential stochastic variational inequalities (DSVIs), in which an ordinary differential equation (ODE) is coupled with history-dependent stochastic variational inequalities (SVI). This framework models closed-loop stochastic systems with time-varying random equilibria and includes optimization-constrained ODEs as special cases. Under appropriate technical conditions, we establish uniqueness, measurability, and Lipschitz continuity with respect to the state of the second-stage response, and consequently the existence and uniqueness of the induced state trajectory. Moreover, we construct a sample average approximation (SAA) based on independent sample paths and prove uniform convergence of the approximate trajectories. For transfer between related stochastic environments, we derive a local $1/2$-Hölder estimate for parametric variational inequalities with moving feasible sets and a quantitative trajectory-stability bound in terms of the initial-state difference and the Wasserstein distance between exogenous path laws. Numerical experiments illustrate the SAA convergence and transfer-stability results. We further apply the framework to an elderly-health monitoring system. Similarity-weighted reuse of precomputed responses achieves an accuracy close to the full-recomputation benchmark of 0.97, while reducing the online batch runtime from 86 seconds to less than one second. Perturbation and delayed-update experiments additionally characterize robustness to sensor noise and the trade-off between response freshness, predictive accuracy, and computational cost. These results provide theoretical and computational support for efficient transfer learning in history-dependent DSVI systems.

This article applies dynamic integral quadratic constraints (IQCs) to the analysis and synthesis of accelerated stochastic gradient algorithms. We consider composite objective functions whose gradient can be approximated via mini-batch sampling and we model the resulting stochastic gradient oracle as a feedback nonlinearity in the spirit of Lur'e systems from robust control. Our first main contribution is a family of IQCs that characterize the second-order statistics of mini-batch gradients, extending the classical Zames–Falb multipliers. Our second contribution is a semidefinite-program for certifying exponential convergence rates of stochastic gradient algorithms, and a complementary condition for bounding the asymptotic variance caused by non-vanishing gradient noise. Our third contribution is a convex synthesis procedure that identifies mini-batch gradient algorithms with the smallest certifiable convergence rate.

Estimating the parameters of an achievement scalarising function is a challenging task in multiobjective optimisation. Achievement scalarising functions are widely used in several contexts, including preference-based optimisation methods and algorithmic procedures for generating or selecting efficient solutions. However, their effectiveness strongly depends on the appropriate specification of their parameters, such as weights and reference points. In this paper, we propose an ordinal-regression-based methodology to estimate the parameters of an achievement scalarising function from preference information provided by the DM. In particular, the proposed approach allows us to infer both the weights associated with the objectives and the reference points characterising the scalarising function. The methodology is illustrated through a didactic example based on a multiobjective knapsack problem, which shows step by step how the preference information is translated into model parameters. The example illustrates that ordinal regression provides a flexible and interpretable framework for calibrating achievement scalarising functions and supporting the elicitation of decision-maker preferences in multiobjective optimisation.

Two-stage distributionally robust optimization chooses a here-and-now decision and a wait-and-see decision policy that adapts to uncertainty realizations. Decision-rule methods specify the form of this adaptive policy in advance, whereas decomposition-generation methods construct second-stage value information iteratively. We connect these approaches through extreme points of the second-stage dual problem. Each extreme point defines an affine value piece, and a compatible primal basis can define an affine policy piece. Solving the first-stage problem may require only a subset of these pieces. We specialize an extreme-point generation method to solve the first-stage problem. A separate linear-programming procedure adds pieces until it recovers the recourse value over the uncertainty set, and the pieces can also be used to recover the optimal recourse policy. Building on the algorithm output, we develop a posteriori exactness test for conventional decision rules. We give extensions for degeneracy, rank-deficient recourse, and structured random recourse. The proposed algorithm is computationally efficient on the reported instances, and the results show that completing the second-stage value across the uncertainty set requires more extreme points than solving the first-stage problem alone.

In this paper we apply the method of Kosygina, Rezakhanlou and Varadhan (CPAM 2006) to establish stochastic homogenization of Hamilton-Jacobi-Bellman (HJB) equation with a vanishing non-local integro-differential operator and a convex super-linearly growing Hamiltonian in stationary ergodic random medium. Their method, first designed for homogenization of HJB equations with vanishing Laplacian operator, relies on stochastic optimal control representation of the solution, a key construction of approximate super-correctors and the technique of linking diffusion process to abstract diffusion in random media. We show how the procedures can be carried out for HJB equations with jump-diffusion. In particular, for the construction of approximate super-correctors, we represent the non-local integro-differential operator as the divergence of a regular integral operator acting on the gradient.

We study online multi-level aggregation on finite rooted trees with a per-batch maximum-delay objective. A service pays for a rooted subtree and for the maximum waiting time among the requests cleared by that service. We show that the offline optimum admits a consecutive-arrival-block normal form and can be computed by a polynomial-time dynamic program. The same dynamic program defines the deadlines of a family of online algorithms, which we call DP-Envelope. Its deterministic endpoint is $2$-competitive. Sampling one global parameter with density $e^\theta/(e-1)$ leads to an $e/(e-1)$-competitive randomized algorithm against an oblivious adversary. The deterministic guarantee matches the known fixed-node lower bound, and we prove a matching randomized lower bound. Thus, both guarantees are optimal on every nondegenerate rooted tree. We first develop the line metric as a warm-up, where the algorithm and its nested block partitions have a direct geometric interpretation. Finally, we show that the upper bounds extend to every realizable static service system with a normalized, nondecreasing, submodular joint service cost.

We study deterministic Riemannian $p$-th-order oracle complexity (for $p\ge2$) on Hadamard manifolds, under strong horospherical ($h$)-convexity and strong geodesic ($g$)-convexity. The two notions agree in the Euclidean space. On a curved Hadamard manifold, $h$-convexity is a stronger notion than $g$-convexity and supplies global horospherical information. Writing the $p$-th-order condition parameter $Q_p=L_pR^{p-1}/\mu$, we obtain the Euclidean-optimal rate $Q_p^{2/(3p+1)}$ for strongly $h$-convex objectives on every Hadamard manifold, with a matching fixed-curvature lower bound. On hyperbolic space, the resulting horoball supports enable localization to the curvature scale. This replaces the condition parameter $Q_p$ by $Q_p \min\{1, 4/(\kappa R) \}^{p-1}$, subject to a logarithmic localization cost. Thus growing negative curvature ($\kappa R \rightarrow \infty$) can further improve the optimal Euclidean rate under $h$-convexity. For strongly $g$-convex objectives, matching upper and lower bounds recover the same Euclidean exponent when $\kappa R=O(1)$. In contrast, with growing $\kappa R$, we construct a hard family on the hyperbolic space with $Q_p\asymp_p(1+\kappa R)^p$ that requires $\widetilde{\Omega}_p(Q_p^{1/p})$ queries. This reveals a fundamental separation: the same hyperbolic divergence that sharpens horoball localization yields an information-theoretic obstruction for the full $g$-convex class.

We study a deterministic family of sharpness-aware minimization methods for smooth nonconvex functions. The perturbation is $$ y_k=x_k+\rho\, \frac{\nabla f(x_k)}{\norm{\nabla f(x_k)}^\alpha}, \qquad 0\leq\alpha\leq 1, $$ so that its effective radius is $\rho\norm{\nabla f(x_k)}^{1-\alpha}$. For $0<\alpha\leq1$, we give an explicit complexity bound above the stationarity level $(L\rho)^{1/\alpha}$. A one-dimensional quadratic example reaches this level exactly, showing that the bound describes a real limitation of the constant-parameter rule. The unnormalized case $\alpha=0$ is treated separately and requires $L\rho<1$. We then introduce a clipped rule which agrees with the constant-$\rho$ rule away from stationary points and becomes proportional to the gradient near them. The clipped method has $\norm{\nabla f(x_k)}\to0$ and the usual $O(T^{-1/2})$ stationarity bound. Numerical tests on a quadratic function, the Rosenbrock function, and a five-dimensional nonconvex function illustrate the stationarity floor of the unclipped rule and the effect of clipping.

Machine learning and optimization have advanced together, with practical demands motivating new theory and theoretical breakthroughs enabling new applications. Modern large-scale training relies on classical optimization principles, but the constraints of distributed systems require these foundations to be reconsidered. This thesis addresses seven challenges at the intersection of theory and practice, focusing on key bottlenecks in federated learning and distributed optimization. First, we introduce ProxSkip and prove that local gradient steps can accelerate communication, providing a theoretical foundation for this widely used heuristic. Second, we develop Variance Reduced ProxSkip, which eliminates the neighborhood error of stochastic local updates while balancing communication and local computation. Third, we show that local steps retain their communication acceleration under partial client participation. Fourth, we prove that server-side stepsizes and sampling without replacement improve convergence in heterogeneous settings. Fifth, for Random Reshuffling, we demonstrate that compressing gradient differences rather than gradients yields better theoretical and practical performance. Sixth, we establish that Byzantine robustness and partial participation can be achieved simultaneously using gradient-difference clipping. Finally, we develop the first theoretical framework for low-rank adaptation based on randomized asymmetric chains, providing new insights into fine-tuning large models. Across these contributions, we introduce novel algorithmic frameworks, establish sharp guarantees under realistic assumptions, and support the theory with numerical experiments.

The Mahalanobis distance is a fundamental covariance-adapted metric for multivariate data and plays a central role in recovering latent geometry from nonlinear observations. We extend this principle from vector-valued data to probability measures by introducing a Wasserstein Mahalanobis distance. Our construction replaces Euclidean displacement vectors with optimal transport displacement fields and local covariance matrices with covariance operators defined on Wasserstein tangent spaces. We show that this construction inherits the geometry-recovery property underlying nonlinear independent component analysis. In particular, for Gaussian measures with common covariance transformed by a smooth nonlinear pushforward, the proposed Wasserstein Mahalanobis distance approximates the classical Mahalanobis distance between the transformed latent means. The correspondence is exact for affine transformations and holds up to controlled higher-order error terms for general smooth transformations. These results establish a distribution-valued analog of classical Mahalanobis geometry and provide theoretical support for covariance-adapted learning directly in Wasserstein space. Numerical experiments confirm the theoretical predictions and demonstrate accurate recovery of latent geometric structure.

Distributionally robust Markov decision processes provide a principled framework for sequential decision making under model uncertainty. We study how many samples are necessary and sufficient to learn an $\varepsilon$-optimal robust policy under the average-reward criterion. A generative model provides samples from the nominal transition kernel, whereas policy performance is evaluated over $(s,a)$-rectangular total-variation uncertainty sets of radius at most $\sigma$. Let $H_0$ and $H_\sigma$ denote the nominal and robust optimal bias spans, respectively. We identify $\sigma H_0$ as the perturbation scale separating high- and low-tolerance regimes. Our matching upper and lower bounds show that, up to logarithmic factors, the minimax total sample complexity is $$ NSA \asymp \frac{SA}{\varepsilon^2}\begin{cases} \min\{H_0,H_\sigma\}, & \varepsilon\gtrsim\sigma H_0,\\ \min\{H_0,H_\sigma\}+\sigma H_\sigma^2, & \varepsilon\lesssim\sigma H_0. \end{cases} $$ Here $S$ and $A$ are the numbers of states and actions, and $N$ is the number of samples per state-action pair. The sample complexity consists of a linear-span term that resembles the nominal AMDP results and a robustness-specific term that appears only in the low-tolerance regime. We attain these rates using reduction-based plug-in procedures that select the reduction—nominal or robust—and its discount factor: a span-informed procedure that makes these choices using known span parameters, and a span-agnostic procedure that calibrates both choices from data.

Artificially introducing a delay in the observations of a system can be an effective mechanism to mask the system itself, with the goal to increase its opacity and thus its security. This work investigates opacity in discrete event systems with delayed observations. We focus on two questions: how to verify opacity under delayed observations, and how to synthesize sensor activation policies that guarantee opacity under such delayed conditions. To address these questions, we first introduce the definition of opacity under delayed observation and develop a corresponding verification method. We then extend such analysis tool into a synthesis tool by proposing an optimization approach for designing sensor activation policies guaranteeing opacity under delayed observations. An example is used to illustrate the analysis and synthesis procedures.

Increasing penetration of inverter-based resources in today's power systems requires substitution of the contribution from synchronous generators to dynamic voltage stability and inertial response. However, established approaches for power system planning are sequential, as stabilising measures are only considered at a later stage of the planning process. We investigate the advantages of an integrated approach for power system planning, where stabilising measures are considered simultaneously with the expansion of generation, transmission, and storage systems via simplified stability constraints on inertia and voltage stability. We find that system costs are reduced with the integrated approach and that the dual-use option of grid-forming battery energy storage systems is favoured over other stabilising measures like static synchronous compensators.

Fault diagnosis and prognosis in discrete event systems are studied in the scenario where the observations are possibly received with delay. To address this scenario, two conditions for diagnosis and prognosis with delayed observations are proposed, where we show that the state-of-the-art notion of prognosability must be revised to avoid conservativeness. Diagnosability and prognosability conditions are then verified by introducing a delay observer and a new verification function. Theoretical analysis indicates the effectiveness of the verification method for fault diagnosis and prognosis in the system.

We study the problem of sampling from target distributions whose potentials are simultaneously non-smooth, subject to superlinear gradient growth, and non-convex. We introduce the Subgradient Tamed Unadjusted Langevin Algorithm (SG-TULA), a discretisation of the Langevin diffusion that operates directly on subgradients, without relying on computationally demanding smoothing procedures. To handle the superlinear regime, taming techniques are employed to produce a stable, explicit scheme. We derive non-asymptotic convergence bounds in Wasserstein-2 distance, with all constants tracked explicitly in terms of dimension and inverse temperature, improving upon the currently known rates for subgradient-based Langevin algorithms. We further provide excess risk estimates for the associated optimisation problem. We verify the assumptions, with explicit constants, for the regularized pretraining potential of a LLM in the GPT-2 lineage and the boosted coordinate-wise variant of SG-TULA pretrains the former competitively against finetuned AdamW and Muon, for which no comparable non-asymptotic guarantees are presently available.

We study stabilization of multidimensional continu- ity equations with source terms on bounded domains by means of localized interior flux feedback. The feedback is prescribed through the divergence of the flux and is chosen so that the error with respect to a reference profile satisfies a transport equation with localized damping. The main geometric condition is a finite-time characteristic damping inequality, requiring relevant characteristics to accumulate a uniform amount of damping over a time horizon. This condition is shown to yield exponential stability in L2 of the error, under a gain condition relating localized damping to compressive amplification of the transport field. Lyapunov-type entrance conditions ensure characteris- tic damping on support-restricted families of trajectories. A weighted Lyapunov functional provides a differential Lyapunov criterion and an input-to-state (ISS) estimate with respect to additive perturbations. We also discuss elliptic right-inverse realizations of the feedback flux and extend the characteristic damping argument to velocity fields depending nonlinearly on the state. A two-dimensional example finally illustrates the geometric, gain, and realization conditions.

We study Muon, a recently proposed matrix-aware optimization method, in the context of the Stiefel manifold. This manifold consists of matrices with orthonormal columns and is ubiquitous in machine learning and scientific computing. Existing extensions of Muon to this manifold rely on heuristic, approximate, or iterative updates with varying computational efficiency. We show that the corresponding Stiefel Muon update admits an exact closed-form solution and use this result to develop Skewon, a practical algorithm for orthogonality-constrained optimization with an efficient implementation. We further establish first-order convergence guarantees for Skewon in the smooth non-convex setting.

In this paper, we build upon the analysis initiated by Gennadiy Averkov and Matthias Schymura (2022) and establish that the number of distinct columns of a $\Delta$-modular matrix $A \in \mathbb{Z}^{m \times n}$ of rank $m$ is $O(m^3 \Delta)$. This upper bound was previously known only for odd values of $\Delta$. Recall that a matrix is called $\Delta$-modular if the maximum of the absolute values of its $m \times m$ minors equals $\Delta$.

A framework is developed for the inference of dynamics described by a generalized system of ordinary differential equations. A stochastic gradient method is coined that infers dynamics from observed marginal probability density functions using the joint probability density function of the observable and latent variables. Diffusion and other irreversible processes observed in a low-dimensional state can be recast as deterministic, reversible flows in a sufficiently augmented state space, where the joint density satisfies the hyperbolic Liouville equation. The marginal distribution observed is the projection of these hyperbolic dynamics onto the observed coordinates, with the latent components carrying the randomness and memory. This reframing allows inference for irreversible or stochastic dynamics into the recovery of a deterministic Ordinary Differential Equation (ODE) from marginal observations. Instead of solving the high-dimensional Liouville equation for the joint density, the algorithm exploits its characteristic representation. Particles sampled from the initial distribution are transported along characteristic lines. The Eulerian sensitivity with respect to parameters is obtained by sensitivity propagation along the characteristic lines, with a crossed U-statistic producing an unbiased gradient estimator, which enables stochastic gradient descent. Four experiments validate the method: recovery of a three-mode linear system observed through the marginal of a single mode; a nonlinear Gompertz growth model with a hidden mode; a bistable system whose hidden mode turns a unimodal marginal bimodal; and Stokes–Oseen drag law recovery for particles in a cellular flow. Convergence behavior is analyzed across these settings.

We study stochastic extragradient (SEG) methods for solving monotone variational inequality problems (VIPs) over a feasible set. Although extragradient is a foundational algorithm for VIPs and its deterministic convergence theory is well developed, its stochastic counterpart remains less understood. Most existing analyses focus on independent-sample SEG (I-SEG) and assume either that the domain is compact or that the variance of the stochastic operator is uniformly bounded. The behavior of same-sample SEG (S-SEG), a natural variant with materially different properties, has received far less attention. In this work, we address these gaps in the literature. We first show that S-SEG is sensitive to samplewise Lipschitz parameters: mean Lipschitzness and bounded variance alone do not ensure convergence, even on a compact set. Then, for possibly unbounded domains, we establish a high-probability restricted-gap convergence for each SEG variant under a relaxed set of assumptions, and show that certain fundamental improvements to these results are impossible in general. Finally, we show that a known asymmetric double step-size selection that guarantees almost sure last-iterate convergence for I-SEG can fail for S-SEG: there exists a stochastic monotone VIP for which S-SEG diverges almost surely even under the modified step-sizes.

We determine the exact weak limited augmented Zarankiewicz numbers $z_{wL}(m,3)$ for all $m\ge 3$: \[ z_{wL}(m,3)= \begin{cases} m+3+\left\lceil \dfrac{m}{2}\right\rceil+1, & 9\le m\le 15,\\[2mm] m+3+\left\lfloor \dfrac{2m-4}{3}\right\rfloor, & m\ge 16, \end{cases} \] with $z_{wL}(3,3)=6$, $z_{wL}(4,3)=8$, and $z_{wL}(m,3)=2m$ for $5\le m\le 9$. In particular, \[ \lim_{m\to\infty} \frac{z_{wL}(m,3)}{m} = \frac{5}{3}. \] The proof is fully analytic, relying on a uniform base classification, two constructive lower-bound families (staircase and $5m/3$), and a sharp upper-bound argument based on a peeling lemma and the analysis of two W2-sensitive boundary cases. Numerical MILP computations were used only as proof-mining tools to identify the structural lemmas; the final theorem is unconditional. We also extend the known range of the original limited numbers $z_L(m,3)$ through $m=13$, where the gap to $z_{wL}(m,3)$ is only 2 or 3.

This note studies the distributed fault diagnosis problem in partially-observed discrete event systems, where the system is monitored by a group of agents to cooperatively diagnose faults within a finite number of steps. The novelty of this work is the creation of a methodology to verify when the faults can be diagnosed even in the presence of transmission delay impairments. To address this scenario, a new distributed diagnosability condition is proposed, which extends decentralized diagnosability conditions proposed in the literature. Such distributed diagnosability condition is then verified via a novel structure named delay recorder and a new diagnosis function. Theoretical analysis shows that the verification method can successfully determine whether the faults can be diagnosed.

Policy iteration (PI) is an important reinforcement learning tool for solving optimal control problems which includes an initialization stage, i.e., the search for an initial stabilizing controller. However, the initialization stage typically relies on complete model information, thereby imposing substantial constraints on the initialization of model-free PI. For stochastic systems with multiplicative noise dependent on state and control, the stability is not ensured by Hurwitz conditions as in the deterministic case, but rather by a Lyapunov-type inequality that incorporates both drift and diffusion terms. Therefore, the corresponding model-free PI initialization problem is more challenging. To this end, a novel spectrum assignment method is proposed to obtain an initial stabilizer for PI in continuous-time indefinite stochastic linear quadratic control. With the help of the Lyapunov-type operator's spectrum, the original system is gradually approximated from the stable auxiliary system by adjusting a cumulative factor, thereby obtaining a stabilizing control gain. Furthermore, by leveraging system data and adjusting the cumulative factor, we design a model-free algorithm that does not rely on an initial stabilizing policy and can achieve optimal control. Finally, simulation results are provided to validate the effectiveness of the proposed methods.

Bi-level interdiction models are frequently solved by metaheuristics whose solution quality cannot be assessed, because exact optima are unavailable at the scales tested. We supply them for the bi-level dual-defense attacker model (BDAM), which couples node interdiction, edge destruction and capacitated supply support, and which we previously solved by a hybrid metaheuristic. First, BDAM's dominant attacker-path term admits an exact single-level reformulation by lower-level dualization, a reduction available whenever arc lengths are linear in the defender's binary decisions; the resulting mixed-integer program certifies optimality on all eighteen three-row and five-row configurations of our earlier benchmark, seventeen in under ten seconds, with strong uncertified incumbents out to 15*30 grids. Our published averages sit 3.55% below that frontier, and the gap widens with scale. Second, the supply rule, like any rule priced on a single attacker shortest path, is ill-posed under ties, and our threat-corridor formulation is tie-invariant by construction. The tie-break moves the objective by under 10^(-3) but the realized supply cost by up to 0.83 units, so the defect is suppressed by the objective weight rather than absent. Third, MILP-DA pairs the exact anchor with the corridor decode and a feasibility repair; compared against our published figures with no re-implementation on either side, it wins on thirteen of eighteen certified configurations and on all eighteen larger ones, every loss falling on a three-row grid.

Neural and numerical policy solvers can produce feasible controls even when the optimal rule and its binding constraints are unavailable. A primal-dual bracket certifies value loss, but it does not locate the optimal policy or explain which constraints genuinely bind. We show that, on the same declared simulation grid, one bracket can support both conclusions. For polyhedral controls, an exact conditional budget identity rewrites the residual as a pathwise nonnegative terminal Fenchel defect plus date-by-constraint complementary-slackness terms. A canonical Doob compensation removes the budget martingale that obscures small residuals. Bellman-primitive curvature conditions then yield an occupancy-weighted policy region with the sharp O(sqrt(G)) radius, while a paired constraint relaxation lower-bounds the optimal multiplier and certifies a binding face. A finite-sample resolution theorem quantifies the path budget needed to certify a target policy tolerance or face. Locked one-asset and two-asset audits cover every external policy error and make no false face declaration. An exact-wrapper stress test remains tight through 50 assets, while a separate state-dependent pilot identifies learned-dual tightness as the high-dimensional bottleneck. Reference solutions enter only after certification.

This article presents a priority-aware robust coverage optimization framework for an aerial sensor network under sensor location uncertainty. Each region is assigned a priority weight, and the objective is to maximize the weighted coverage while maintaining robustness against positional perturbations. A mathematical optimization model is developed by incorporating surveillance constraints and an RRF-based robustness formulation into the proposed framework. An efficient priority-aware robust orientation optimization (PAROO) algorithm is then proposed to determine the sensor orientations that maximize the weighted coverage objective. Experimental results on an airport-inspired surveillance scenario demonstrate that the proposed framework effectively directs sensing resources toward high-priority regions and achieves higher weighted coverage than representative baseline approaches, highlighting its practical applicability in security-sensitive environments.

The degree sequence optimization problem is to find a subgraph of a given graph which maximizes the sum over all vertices of a given function evaluated at the subgraph degree of that vertex. Here we study this problem and its complexity for quadratic functions. In particular, we introduce the critical roots of a graph, and show they define intervals over which the optimal value of the problem, as the quadratic root varies, is convex piecewise affine.

We study the identification of effective coefficients for wave equations in heterogeneous media. Such equations arise in the modeling of spatio-temporal metamaterials, where the underlying material properties exhibit variations in both space and time. While homogenization provides effective models in the asymptotic regime of vanishing microscopic scales, determining macroscopic parameters from observations of wave propagation remains challenging. We introduce an optimization-based method that identifies a constant effective coefficient by minimizing a cost functional. The approach is designed for situations in which the underlying space-time-dependent coefficient is unknown, while the solution is available in space and time by measurements. We extend optimization-based coefficient identification techniques from elliptic multiscale problems to wave equations and prove that, provided a homogenized limit exists, the identified coefficient converges to the homogenized coefficient as the microscopic scale tends to zero. Furthermore, we establish convergence of the corresponding effective solution towards the heterogeneous solution, including strong convergence in $L^2$ and weak convergence of first-order space and time derivatives. Numerical experiments further demonstrate the performance of the method for non-periodic space-time heterogeneous media, including cases for which a homogenized limit is not known to exist.

Constrained density functional theory (CDFT) provides a powerful framework for describing electronically excited and charge-localized states, which underlie a broad range of physical and chemical phenomena. However, the discretized optimization problems arising from CDFT calculations remain challenging, owing to the presence of both the Stiefel manifold constraint and additional nonconvex quadratic constraints. Existing algorithms either fail to enforce the quadratic constraints with high accuracy or face convergence issues due to double-loop iterative structures. In this paper, we first derive a subspace-splitting reformulation that decouples the two groups of constraints, by exploiting the inherent rotation invariance and introducing a nonlinear subspace alignment constraint. Based on this reformulation, we propose a single-loop damped alternating direction method of multipliers, called DASSP. To the best of our knowledge, DASSP is the first algorithm for CDFT calculations with rigorous convergence guarantees. Each iteration of DASSP comprises a spectral minimization step, a projected gradient step, and a damped dual ascent step, all of which admit efficient implementations. Numerical results on synthetic and realistic CDFT problems demonstrate that DASSP attains high feasibility accuracy and exhibits favorable efficiency without compromising robustness. We expect that this work will pave the way toward reliable and efficient large-scale CDFT applications.