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Semi-infinite Nonconvex Constrained Min-Max Optimization
Cody Melcher, Zeinab Alizadeh, Lindsey Hiett, Afrooz Jalilzadeh, Erfan Yazdandoost Hamedani
https://arxiv.org/abs/2510.12007

Semi-infinite Nonconvex Constrained Min-Max Optimization
Semi-Infinite Programming (SIP) has emerged as a powerful framework for modeling problems with infinite constraints, however, its theoretical development in the context of nonconvex and large-scale optimization remains limited. In this paper, we investigate a class of nonconvex min-max optimization problems with nonconvex infinite constraints, motivated by applications such as adversarial robustness and safety-constrained learning. We propose a novel inexact dynamic barrier primal-dual algorith…

Linear Convergence of a Unified Primal--Dual Algorithm for Convex--Concave Saddle Point Problems with Quadratic Growth
Cody Melcher, Afrooz Jalilzadeh, Erfan Yazdandoost Hamedani
https://arxiv.org/abs/2510.11990

Linear Convergence of a Unified Primal--Dual Algorithm for Convex--Concave Saddle Point Problems with Quadratic Growth
In this paper, we study saddle point (SP) problems, focusing on convex-concave optimization involving functions that satisfy either two-sided quadratic functional growth (QFG) or two-sided quadratic gradient growth (QGG)--novel conditions tailored specifically for SP problems as extensions of quadratic growth conditions in minimization. These conditions relax the traditional requirement of strong convexity-strong concavity, thereby encompassing a broader class of problems. We propose a generali…

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