arXiv subjects

Zeinab Alizadeh

Publications and source records attributed to Zeinab Alizadeh.

9 recordsLinked to original sources

arXiv2026

Regularized Projection Algorithms for Monotone Inverse Variational Inequalities

Stochastic inverse variational inequalities (SIVIs) arise in applications in which equilibrium responses are observed under uncertainty, such as inverse road pricing and network equilibrium control. Existing methods typically rely on co-coercivity or strong monotonicity, while general monotone SIVIs remain less understood. We propose a regularized projection algorithm that combines Tikhonov regularization with increasing batch sizes. Under monotonicity and Lipschitz continuity, we prove almost sure boundedness of the iterates and almost sure convergence of their distance to the SIVI solution set. We further establish, to the best of our knowledge, the first explicit nonasymptotic rate of $O(T^{-1/2})$ for the expected squared residual under general monotonicity. This yields $O(ε^{-2})$ iterations and $O(ε^{-4-2δ})$ stochastic oracle calls, for any $δ>0$, to obtain an $ε$-solution in expected squared residual. A deterministic variant attains the same iteration complexity using $O(ε^{-2})$ exact operator evaluations. Numerical experiments illustrate the proposed methods on monotone SIVI problems.

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arXiv2025

Convergence Analysis of Non-Strongly-Monotone Stochastic Quasi-Variational Inequalities

While Variational Inequality (VI) is a well-established mathematical framework that subsumes Nash equilibrium and saddle-point problems, less is known about its extension, Quasi-Variational Inequalities (QVI). QVI allows for cases where the constraint set changes as the decision variable varies allowing for a more versatile setting. In this paper, we propose extra-gradient and gradient-based methods for solving a class of monotone Stochastic Quasi-Variational Inequalities (SQVI) and establish a rigorous convergence rate analysis for these methods. Our approach not only advances the theoretical understanding of SQVI but also demonstrates its practical applicability. Specifically, we highlight its effectiveness in reformulating and solving problems such as generalized Nash Equilibrium, bilevel optimization, and saddle-point problems with coupling constraints.

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arXiv2025

Distributionally Robust Nash Equilibria via Variational Inequalities

Nash Equilibrium and its robust counterpart, Distributionally Robust Nash Equilibrium (DRNE), are fundamental problems in game theory with applications in economics, engineering, and machine learning. This paper addresses the problem of DRNE, where multiple players engage in a noncooperative game under uncertainty. Each player aims to minimize their objective against the worst-case distribution within an ambiguity set, resulting in a minimax structure. We reformulate the DRNE problem as a Variational Inequality (VI) problem, providing a unified framework for analysis and algorithm development. We propose a gradient descent-ascent type algorithm with convergence guarantee that effectively addresses the computational challenges of high-dimensional and nonsmooth objectives.

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arXiv2025

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 algorithm and establish its convergence properties. Specifically, under the assumption that the squared infeasibility residual function satisfies the Lojasiewicz inequality with exponent $θ\in (0,1)$, we prove that the proposed method achieves $\mathcal{O}(ε^{-3})$, $\mathcal{O}(ε^{-6θ})$, and $\mathcal{O}(ε^{-3θ/(1-θ)})$ iteration complexities to achieve an $ε$-approximate stationarity, infeasibility, and complementarity slackness, respectively. Numerical experiments on robust multitask learning with task priority further illustrate the practical effectiveness of the algorithm.

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arXiv2025

Variance-reduction for Variational Inequality Problems with Bregman Distance Function

In this paper, we address variational inequalities (VI) with a finite-sum structure. We introduce a novel single-loop stochastic variance-reduced algorithm, incorporating the Bregman distance function, and establish an optimal convergence guarantee under a monotone setting. Additionally, we explore a structured class of non-monotone problems that exhibit weak Minty solutions, and analyze the complexity of our proposed method, highlighting a significant improvement over existing approaches. Numerical experiments are presented to demonstrate the performance of our algorithm compared to state-of-the-art methods

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arXiv2023

A Projection-Based Algorithm for Solving Stochastic Inverse Variational Inequality Problems

We consider a stochastic Inverse Variational Inequality (IVI) problem defined by a continuous and co-coercive map over a closed and convex set. Motivated by the absence of performance guarantees for stochastic IVI, we present a variance-reduced projection-based gradient method. Our proposed method ensures an almost sure convergence of the generated iterates to the solution, and we establish a convergence rate guarantee. To verify our results, we apply the proposed algorithm to a network equilibrium control problem.

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arXiv2023

Accelerated Primal-dual Scheme for a Class of Stochastic Nonconvex-concave Saddle Point Problems

Stochastic nonconvex-concave min-max saddle point problems appear in many machine learning and control problems including distributionally robust optimization, generative adversarial networks, and adversarial learning. In this paper, we consider a class of nonconvex saddle point problems where the objective function satisfies the Polyak-Łojasiewicz condition with respect to the minimization variable and it is concave with respect to the maximization variable. The existing methods for solving nonconvex-concave saddle point problems often suffer from slow convergence and/or contain multiple loops. Our main contribution lies in proposing a novel single-loop accelerated primal-dual algorithm with new convergence rate results appearing for the first time in the literature, to the best of our knowledge. In particular, in the stochastic regime, we demonstrate a convergence rate of $\mathcal O(ε^{-4})$ to find an $ε$-gap solution which can be improved to $\mathcal O(ε^{-2})$ in deterministic setting.

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arXiv2023

Randomized Lagrangian Stochastic Approximation for Large-Scale Constrained Stochastic Nash Games

In this paper, we consider stochastic monotone Nash games where each player's strategy set is characterized by possibly a large number of explicit convex constraint inequalities. Notably, the functional constraints of each player may depend on the strategies of other players, allowing for capturing a subclass of generalized Nash equilibrium problems (GNEP). While there is limited work that provide guarantees for this class of stochastic GNEPs, even when the functional constraints of the players are independent of each other, the majority of the existing methods rely on employing projected stochastic approximation (SA) methods. However, the projected SA methods perform poorly when the constraint set is afflicted by the presence of a large number of possibly nonlinear functional inequalities. Motivated by the absence of performance guarantees for computing the Nash equilibrium in constrained stochastic monotone Nash games, we develop a single timescale randomized Lagrangian multiplier stochastic approximation method where in the primal space, we employ an SA scheme, and in the dual space, we employ a randomized block-coordinate scheme where only a randomly selected Lagrangian multiplier is updated. We show that our method achieves a convergence rate of $\mathcal{O}\left(\frac{\log(k)}{\sqrt{k}}\right)$ for suitably defined suboptimality and infeasibility metrics in a mean sense.

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arXiv2022

An Inexact Variance-Reduced Method For Stochastic Quasi-Variational Inequality Problems With An Application In Healthcare

This paper is focused on a stochastic quasi-variational inequality (SQVI) problem with a continuous and strongly-monotone mapping over a closed and convex set where the projection onto the constraint set may not be easy to compute. We present an inexact variance reduced stochastic scheme to solve SQVI problems and analyzed its convergence rate and oracle complexity. A linear rate of convergence is obtained by progressively increasing sample-size and approximating the projection operator. Moreover, we show how a competition among blood donation organizations can be modeled as an SQVI and we provide some preliminary simulation results to validate our findings.

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