Month: August 2026
Solving Quasi-Variational Inequalities Using the Progressive Decoupling of Linkages
Inspired by the progressive decoupling of linkages methodology for optimization and variational inequalities, we propose an algorithm for solving quasi-variational inequalities as a sequence of variational inequalities. Our method is shown to converge locally under some regularity conditions and globally when such conditions hold throughout the entire domain. Separately, under other type of assumptions, global … Read more
An Adaptive Augmented Lagrangian Method for Deterministic and Stochastic Nonconvex Optimization
We present an inexact Augmented Lagrangian algorithm for solving nonlinear, non-convex optimization problems. Unlike most recently proposed Augmented Lagrangian methods with worst-case complexity guarantees, we utilize adaptive penalty parameter updates and full dual stepsizes. We show that the method matches the best known worst-case complexity results for Augmented Lagrangian methods (up to logarithmic factors) when … Read more
Optimizing Family Medicine Residency Schedules under the Clinic First Principles
Family medicine residency programs must balance educational and operational requirements while providing residents with consistent exposure to continuity clinics, a central principle of the Clinic First Model. We study the Family Medicine Residency Scheduling problem and develop a binary integer programming (BIP) framework that incorporates Clinic First principles through two criteria: Clinic Time Consistency (CTC), … Read more
Sharp Singularity-Degree Bounds for Equality-Generated SDP–RLT Relaxations of Binary Programs
Singularity degree is an important measure of semidefinite programming (SDP) degeneracy, but it is generally unavailable a priori from the problem data. We augment the Shor relaxation of binary sets \(\{x\in\{0,1\}^n:Ax=b\}\) with the first-level Reformulation–Linearization Technique (RLT) equations generated by the defining linear equalities. For the resulting equality-generated SDP–RLT relaxation, we determine the exact worst-case … Read more
Valid Inequalities for Potential-Based Network Design Including Compressors
We study the steady-state expansion problem for potential-based flow networks. Constructing a cost-minimal network that admits a flow satisfying the underlying physical laws is a central problem in the design of gas, hydrogen, water, and electricity infrastructures. The physical behavior of such networks is governed by nonlinear relations between arc flows and the potential differences … Read more
ArcLP: A Matlab implementation of an O(√nL) arc-search infeasible interior-point algorithm for linear programming
This paper presents a Matlab implementation of an arc-search infeasible interior point algorithm for linear programming (LP), which has a proven polynomial bound of O(√nL), the best among all interior-point algorithms for LP. Software architecture and major functions are discussed. Its ease of use is described by a simple example. Crucial strategies are summarized. Quality … Read more
Two Spectral Gaps: Decentralized Optimization over Intersections of Local Convex Sets
We study decentralized minimization of an average of strongly convex, smooth local objectives over an intersection of agent-private closed convex sets, where each agent knows only its own objective and its own set and agents communicate over a gossip network. We show that the complexity is controlled by a single geometric scalar, which we call … Read more
On the exponential circuit imbalance of the Ben-Tal Nemirovski approximation
Dadush et al.\ (2024) recently developed a scaling-invariant layered least squares algorithm for linear programming whose complexity depends on the optimal condition measure $\bar{\chi}_A^*$. Their work builds on Vavasis and Ye’s (1996) algorithm whose running time depends only on the constraint matrix $A$ through the condition number $\bar{\chi}_A$. Monteiro-Tsuchiya (2003) defined the optimal condition number … Read more
Implicit Primal-Dual Guarantees in Unconstrained First-Order Minimization
This work considers the design of first-order convex optimization algorithms and convergence proofs. In particular, we consider nonsmooth Lipschitz and smooth problems accessed through a subgradient or gradient oracle, respectively. For the general class of fixed-step first-order methods, prior work on Performance Estimation Problems (PEPs) has shown that structured, tight convergence proofs typically exist. Under … Read more