295 papers
This paper introduces a two-stage stochastic capacity expansion model for many-to-one matching markets that accounts for both exogenous preference uncertainty and endogenous strategic misreporting, proposing sample average approximation-based heuristics to optimize school capacities and improve student outcomes compared to deterministic approaches.
This paper proposes a simple, merit-function-free first-order algorithm for full-rank equality constrained optimization that adaptively selects between tangent and infeasibility-reducing steps without evaluating the objective function, achieving an O(1/sqrt{k}) convergence rate and demonstrating robust performance in noisy environments.
This paper establishes the theoretical consistency of sample average approximation and Karush–Kuhn–Tucker conditions for stochastic optimization problems with almost sure conic constraints in infinite-dimensional Banach spaces, providing a rigorous foundation for numerical methods across diverse applications such as operator learning, optimal transport, and PDE-constrained optimization.
This paper provides rigorous theoretical guarantees for the existence and uniqueness of physically correct hydraulic states in water distribution systems by solving the underlying non-linear equations, thereby establishing a foundational basis for the reliability of hydraulic simulators and extending beyond previous approximation-based observability analyses.
This paper introduces a unified spectral decomposition system for analyzing spectral functions on Hilbert spaces and establishes a novel reduced minimization principle that constructively simplifies the evaluation of their convex analytical objects, such as conjugates, subgradients, and Bregman proximity operators.
This paper introduces a novel subgradient definition based on Busemann functions for convex optimization on Hadamard spaces, enabling the generalization of stochastic and incremental subgradient methods with guaranteed complexity bounds to nonpositively curved metric spaces such as BHV tree space.
This paper introduces the Alternating Subspace Method (ASM), a novel sparse recovery algorithm that integrates greedy and splitting strategies by enforcing data fidelity within a subspace, thereby guaranteeing global convergence and achieving fast local geometric convergence on LASSO problems while demonstrating high efficiency and flexibility across various applications.
This paper introduces and analyzes the convergence of a proximal-type algorithm with line search and inertial methods for solving DC programs under the Kurdyka-Łojasiewicz property, demonstrating its effectiveness in variable selection for linear regression.
This paper introduces sparse linear inequalities that outer approximate the positive semidefinite cone to create an LP relaxation with bounds equivalent to semidefinite programming, demonstrating that these inequalities can accelerate branch-and-bound algorithms for solving nonconvex quadratic optimization problems.
This paper investigates optimization problems concerning the relationship between the first eigenvalue and torsional rigidity induced by general anisotropic seminorms, specifically analyzing the minimization and maximization of their product functional with respect to the seminorm control.
This paper investigates the well-posedness, simultaneous exact and approximate controllability, and polynomial stabilization of cascade coupled 1-d heat and wave systems within an abstract LTI framework, leveraging the cascade structure to overcome challenges associated with classical energy methods.
This paper contrasts the mathematical structures and optimality conditions of rate-control versus effort-control harvesting in age-structured populations, demonstrating how the multiplicative, aggregate-dependent nature of effort-control introduces nonlocal coupling in the adjoint system that fundamentally distinguishes it from the additive rate-control formulation.
This paper proposes a model-free reinforcement learning algorithm that achieves almost sure convergence with an optimal rate of O(1/n) for solving long-run Conditional Value-at-Risk (CVaR) optimization problems in Markov decision processes using a single sample trajectory.
This paper introduces ALMTON, a globally convergent third-order Newton method for unconstrained nonconvex optimization that achieves an complexity by using adaptive quadratic regularization to maintain a tractable cubic model solvable via a single semidefinite program per iteration, thereby outperforming existing third-order and second-order baselines in convergence consistency and robustness.
This paper surveys averaging techniques in stochastic gradient methods, covering their theoretical foundations, modern developments in machine learning applications, finite-sample behaviors, and future research directions.
This paper refines the understanding of maximal faces in the cone of completely positive matrices by proving that the exact lower bound on their dimensions is for odd , and establishing a new upper estimate between and for even .
This paper proposes an ADMM-based Bilevel Descent Aggregation (ADMM-BDA) algorithm for sparse hyperparameter selection that overcomes the limitations of existing methods by achieving global convergence without relying on the restrictive lower-level singleton assumption.
This paper extends the theory of Lorentzian and completely log-concave polynomials to proper convex cones by defining -Lorentzian forms and associated semipositive cones, establishing their geometric properties and negative-dependence interpretations, and applying these results to derive new Lyapunov stability criteria for cone-constrained evolution variational inequality systems.
This paper presents an optimization-driven, adjoint-based framework that utilizes both monolithic and partitioned strategies to simultaneously identify structural damage and reconstruct temperature fields in one-way thermo-mechanically coupled systems, demonstrating superior accuracy over traditional assumptions even with sparse and suboptimally placed sensor networks.
This paper introduces a Unifying Primal-Dual Proximal (UPP) framework that linearizes the augmented Lagrangian to unify various distributed nonconvex optimization methods, proving sublinear convergence to stationary points and linear convergence under the Polyak-Łojasiewicz condition, while demonstrating superior performance through specialized algorithms like UPP-MC and Chebyshev-accelerated UPP-SC-OPT.