Optimization and Control Papers

ALT A 2BSDE system is written down for a (D+1)-dimensional Black–Scholes partial differential equation (PDE) with the Leland transaction cost model which incorporates the sign of the curvature. The 2BSDE system takes input from the “speed” (derivative of the curvature). This system is solved using a single ResNet neural network which learns both the solution to the PDE as well as the degrees of freedom in the curvature matrix. The network is used to learn the price of derivatives such as call options and butterfly spreads on geometric baskets for D=10,100 achieving a time-averaged RMSE of less than 0.1 in each case.

ALT Childcare shortages have limited families' access to quality care, with consequences for children's development and parents' careers. We link two decades of childcare supply data to longitudinal surveys of U.S. scientists. We find workplace childcare deserts are widespread: more than half of scientists at universities and research institutions work in deserts, where supply falls significantly short of demand. We further find mothers working in deserts are less likely to attain tenure. They are also more likely to move to industry and part-time positions. Reduced work time partly accounts for the tenure association but other reasons remain. Expanding childcare availability near workplaces may help retain scientific talent.

ALT Can learned latent dynamics models support the design of feedback controllers that provably stabilize the original system? For linear time-invariant systems, we show that learning linear autoencoders and latent dynamics with multi-step prediction-reconstruction losses unicodex2014 which we term "backward losses" as they encourage latent trajectories to reconstruct full state trajectories unicodex2014 provably recovers the structure needed for stabilization. Specifically, a sufficiently long reconstruction horizon ensures that a minimum H_∞-norm controller designed using the learned latent model stabilizes the original system through output-feedback via the corresponding encoder, provided the latent dimension is large enough to capture all non-stable modes of the underlying system. We also show why both reconstruction and a multi-step horizon are essential: forward prediction losses that require only low prediction error along latent trajectories admit global loss minimizers that discar

ALT We introduce a fast novel algorithm to commit hydro-generators. We show that our algorithm can commit 56 generators for 200 days 10,000 times faster than Hexaly, the leading commercial solver for scheduling problems, without sacrificing solution quality. Our method can commit 1792 generators for an entire year in approximately 20 seconds on commodity hardware. Hexaly is unable to solve problems of this size in reasonable time. We attain this runtime improvement by introducing a greedy-heuristic tailored for hydro units. We provide a direction for a possible proof that the error our solver makes decreases with the problem size. This is supported by our experimental results. We prove that our solver's runtime scales log-linearly in the number of generators and time periods.

ALT Gradient flows of twice continuously differentiable strongly convex and convex objectives are, respectively, incrementally exponentially stable and non-expansive in the Euclidean metric. In this work, we investigate to what extent these properties extend to nonconvex objectives satisfying generalized Polyak-Łojasiewicz inequalities. For objectives with a unique minimizer, we establish conditions under which the gradient flow is contracting in a state-dependent Riemannian metric and incrementally exponentially stable. For objectives with nonunique minimizers, we generalize the non-expansivity of convex objectives to incremental stability for more general nonconvex objectives. We focus on incremental stability due to its implication to convergence to equilibrium points; when paired with a Lyapunov function it implies pointwise convergence to a minimizer and continuity of the endpoint map. Along the way, we derive new structural results for incrementally stable nonlinear systems and exten

ALT We hereby fill in a gap in an induction argument used in the proof of a theorem on state-covariance controllability of linear stochastic systems in an earlier paper by the authors. The mathematical statement is true. The missing point in the proof concerns the assertion that, in the canonical single-input case, the control can be assigned arbitrary endpoint values. We amend the argument by proving a slightly stronger induction statement that permits arbitrary finite endpoint jets of the control. An independent approach to homogeneous state-covariance controllability was provided in a paper by Abdelgalil and Georgiou (2025) as a corollary of strong controllability results on GLp(n,ℝ), and shown herein that it extends to the case of additive noise as well.

ALT In this work, we study Burer-Monteiro factorizations of semidefinite programs with unit diagonal constraints. For a real symmetric cost matrix whose rank-width over ℝ is at most k, we prove that every non-flat second-order stationary point of the factorized problem is globally optimal whenever the factorization rank is at least 2k, independently of the matrix size.

ALT We study how curvature estimated from gradient differences can accelerate proximal-extragradient quasi-Newton methods. Existing global guarantees for QNPE, A-QNPE, and OL-OQN learn Hessian approximations online and incur dimension dependence through regret bounds. We introduce certified curvature reuse: one finite-difference probe per iteration refreshes a group of Hessian columns, while a path-length certificate controls the error of stale columns and determines the step. Each iteration uses at most three gradient queries and one regularized linear solve (or trust-region step), without a gradient line search or an inner oracle-querying loop. In the convex and strongly convex settings, bisection on stored scalar quantities selects a near-maximal certified stepsize; in the nonconvex setting, a uniform certificate gives an explicit learning rate. With other problem parameters fixed, the convex method attains O(min{k^-2,dk^-3}) in a single run, with no logarithmic factor or additive dimen

ALT Retailers can learn customer preferences by experimenting with different assortments. However, the cost of each experiment and the operational burden of repeatedly changing product offerings can make extensive experimentation impractical. We study how much a retailer can improve its final assortment decision using customer observations from one (or a very small number of) fixed experimental assortments. We consider the multinomial logit model, where product revenues are known but customer preferences are unknown. In this setting, we jointly design the experimental assortment and the rule for selecting a final assortment from observed customer choices to minimize worst-case regret: the expected revenue loss of the final assortment relative to an optimal assortment under the true preferences, maximized over possible customer preferences. We first characterize exactly the minimax regret and an optimal assortment when no experimentation is possible. We then show, surprisingly, that offerin

ALT This paper develops a constrained linear-quadratic (LQ) optimal control framework within the behavioral approach. Unlike classical formulations that rely on state-input representations, our method treats both the system dynamics and the constraints as trajectory-level objects. The system is modeled through a kernel representation, while inequality constraints are captured using behavioral inequalities defined over infinite-dimensional convex cones. Using quadratic differential forms (QDFs) to encode performance indices, we formulate the constrained LQ problem as a convex variational optimization over trajectories. By employing Gateaux differentials, we derive the stationarity and complementarity conditions and show that they admit a representation as an augmented behavioral system whose unique decomposition into autonomous and controllable sub-behaviors yields a complete parameterization of all optimal constrained trajectories. The resulting conditions constitute a behavioral analogue

ALT Ground-state search in two-dimensional Ising spin glasses on large toroidal lattices remains challenging for local-update heuristics because rugged energy barriers impede relaxation across metastable states. Equivalent to zero-field toroidal Max-Cut problems, these spin-glass instances also serve as standard benchmarks for optimization heuristics. Many Monte Carlo approaches combine single-spin flips or cluster moves with temperature ladders or annealing schedules, yet even with tuned parameters, rarely achieve rapid, reliable ground-state convergence at scale. Here, we address the need for faster ground-state search through cooperation between replicas. We introduce ranked greedy cluster exchange (RGCX) and combine it with fixed-temperature Metropolis sweeps to form single-temperature RGCX. Replicas are ranked by cut to determine the pair-processing order. Each pair deterministically exchanges every disagreement cluster that raises the better replica's cut, retaining the complement an

ALT This paper presents a numerical investigation of soft-to-hard terminal constraint convergence for optimal control problems governed by a second-order ordinary differential equation and the one-dimensional heat equation. The study complements the analytical convergence theory through comparisons with exact solutions and independently computed numerical approximations. For the heat equation, a fully discrete Crank–Nicolson finite-difference formulation is validated against exact modal solutions, exhibiting approximately second-order convergence in the terminal-state and midpoint-sampled control errors under simultaneous space-time mesh refinement. Numerical experiments demonstrate the predicted first-order penalty convergence for benchmark problems and investigate the admissibility threshold governing finite-energy exact terminal controllability. Additional modal experiments examine the dependence of terminal-error convergence rates on spectral regularity, illustrating intermediate rates

ALT For a finite empirical target, the exact reverse diffusion is driven toward training points by an attraction whose strength diverges as the forward noising time decreases to zero. We study whether this terminal localization persists under progressively measurable score errors that may themselves be singular. For reverse Ornstein–Uhlenbeck diffusions, from an arbitrary initial law and under a deterministic error envelope E imposed along the perturbed trajectory satisfying t∫ₜᵀ E(σ)/σ dσ→0, we prove almost-sure convergence to a training point, together with explicit uniform bounds on a terminal window with probability arbitrarily close to one. Every training point has positive terminal probability, although the terminal selection probabilities need not match the empirical weights. The results cover power-law errors E(t)=O(t⁻ᵞ), 0<γ<1, including infinite squared-error energy. For suitable errors in this range, the exact and perturbed full path laws can be mutually singular while their ter

ALT We introduce a new class of problems, termed multi-split multiple-sets implicit convex feasibility problems (MSMS-ICFPs), define a proximity function for it and analyze its properties under certain assumptions on the involved general point-to-set operators. Additionally, we discuss its properties for a special class of point-to-set operators. For these kinds of point-to-set operators, we deploy a new iterative algorithm to solve the associated MSMS-ICFP and show that any sequence generated by it converges in norm to a solution of the MSMS-ICFP whenever a solution exists (i.e., in the consistent case). We also define a generalized proximity function for the MSMS-ICFP using the Bregman distance. Based on this function, we present a generalized simultaneous projection gradient algorithm for the split feasibility problem with multiple output sets, by examining various related results. We conclude by discussing several further special cases of the MSMS-ICFP.

ALT In this paper, we propose two iterative methods, the modified Picard method (MPM) and the generalized Traub method (GTM), to solve a new generalized absolute value equation (NGAVE). We establish their convergence under appropriate assumptions. Additionally, numerical examples demonstrate the effectiveness and applicability of the developed algorithms.

ALT We develop an algorithm for computing the convex envelope of the bilinear function f(x,y)=xy over possibly nonconvex polygonal domains. Building on existing methods for convex polytopes, our approach uses the Karush-Kuhn-Tucker conditions and an analysis of the contact points between affine underestimators and the graph of f. Nonconvex domains admit additional contact configurations that prevent several simplifications available in the convex case. We resolve these configurations explicitly and show that the envelope admits a finite polyhedral subdivision with affine, quadratic, or rational expressions on its cells. For orthogonal polygons, whose edges are horizontal or vertical, we establish substantial reductions in the generator sets needed to compute the envelope. We also present methods for constructing such domains as relaxations of two-dimensional projections of nonlinear optimization problems. An illustrative example quantifies the loss in relaxation strength caused by convexif

ALT The standard quadratic optimization problem consists of minimizing a quadratic form over the standard simplex. It has highly relevant applications ranging from portfolio optimization to machine learning. However, if the quadratic form is neither convex nor concave, this problem is NP-hard. We study a distributionally robust chance-constrained variant whose ambiguity set is a Wasserstein ball around the sampled distribution and make four contributions. First, although the problem is nonconvex in the decision variable, we exploit its linear dependence on the uncertain matrix to reduce the problem to a mixed-integer quadratic optimization problem. Second, we show that a judicious choice of matrix norm—the entrywise maximum norm—makes this reformulation both exact and tractable, and we describe the induced worst-case distribution. Third, our formulation is, by construction, the minimization of the worst-case Value-at-Risk of the random quadratic form; this unifies it with existing framewor

ALT This paper addresses the stability analysis of a class of linear infinite-dimensional port-Hamiltonian systems formulated within the variational framework. We derive verifiable conditions for the equivalence of the Hamiltonian-induced energy norm and the natural state-space norm, as well as for the generation of a contraction semigroup by the associated system operator. The semigroup generation result is obtained by establishing dissipativity and verifying the required range condition. The proposed conditions simplify the functional-analytic stability analysis of this class of systems in a manner similar to established results for the Stokes-Dirac setting.

ALT AdaGrad-style methods can simultaneously adapt to both the order and constants of smoothness in centralized optimization. However, existing extensions to federated optimization with heterogeneous client objectives and multiple local steps require the smoothness order to be specified in advance. We address this limitation with AdaFed, a federated method that adapts across several regimes under a single choice of parameters. In the deterministic setting, AdaFed achieves an O(1/T) convergence rate for both smooth nonconvex and smooth convex objectives, and an O(1/√T) rate for Lipschitz nonsmooth convex objectives up to logarithmic factors. Under a light-tailed stochastic-gradient noise assumption, these guarantees extend to the stochastic setting with additional logarithmic factors and noise-dependent terms. Experiments across the three problem classes further support our theoretical findings.

ALT Long-haul truck electrification requires rapid energy replenishment near freight demand, although dispersed hubs may lack sufficient grid capacity. We study a "Swap-Locally, Charge-Centrally" architecture embedded in a relay freight network: swapping remains close to freight flows, charging can be shifted to grid-suitable hubs, and co-location is retained where economical. A multi-period, two-stage stochastic location-inventory-fleet model coordinates station deployment, replenishment assignments and grid-bounded charging capacity with scenario-dependent battery stocks, batch sizes and incremental fleet requirements. Corridor electrification competes with temporary diesel operation. Building on submodularity-based constraint generation for location-inventory systems, we give an alternative scalar partial-minimization proof that the battery value function is submodular, show that the fleet recourse is affine in the binary swap-station decisions, and develop a Lovász-cut Benders decompos