About

Dr. Afrooz Jalilzadeh is an assistant professor at the University of Arizona in the Department of Systems and Industrial Engineering. She is also a member of the Applied Mathematics GIDP and Statistics & Data Science GIDP. Dr. Jalilzadeh received her bachelor's degree in Mathematics from the University of Tehran and earned her Ph.D. in Industrial Engineering and Operations Research from Pennsylvania State University. Her research focuses on designing, analyzing, and implementing stochastic approximation methods to solve convex optimization and stochastic variational inequality problems. These methods have applications in diverse fields including machine learning, game theory, healthcare, and power systems.

Research topics

• Mathematics
• Statistics
• Mathematical analysis
• Combinatorics
• Computer Science
• Geometry
• Mathematical optimization
• Applied mathematics
• Physics

Selected publications

• On the Analysis of Misspecified Variational Inequalities with Nonlinear Constraints

  Zenodo (CERN European Organization for Nuclear Research) · 2026-03-20

  articleOpen accessSenior author

  In this paper, we study a class of misspecified variational inequalities (VIs) where both the monotone operator and nonlinear convex constraints depend on an unknown parameter learned via a secondary VI. Existing data-driven VI methods typically follow a decoupled learn-then-optimize scheme, causing the approximation error from the learning to propagate the main decision-making problem and hinder convergence. We instead consider a simultaneous approach that jointly solves the main and secondary VIs. To efficiently handle nonlinear constraints with parameter misspecification, we propose a single-loop inexact Augmented Lagrangian method that simultaneously updates the primal decision variables, dual multipliers, and the misspecified parameter. The method combines a forward-reflected-backward step with an Augmented Lagrangian penalty, and explicitly handles misspecification on both the operator and constraint functions. Moreover, we introduce a relaxed performance metric based on the Minty VI gap combined with an aggregated infeasibility metric. By proving boundedness of the dual iterates, we establish $\mathcal{O}(1/K)$ ergodic convergence rates for these metrics. Numerical experiments are provided to showcase the superior performance of our algorithm compared to state-of-the-art methods.

  PublisherDOI

• On the Analysis of Misspecified Variational Inequalities with Nonlinear Constraints

  ArXiv.org · 2026-01-31

  articleOpen accessSenior author

  In this paper, we study a class of misspecified variational inequalities (VIs) where both the monotone operator and nonlinear convex constraints depend on an unknown parameter learned via a secondary VI. Existing data-driven VI methods typically follow a decoupled learn-then-optimize scheme, causing the approximation error from the learning to propagate the main decision-making problem and hinder convergence. We instead consider a simultaneous approach that jointly solves the main and secondary VIs. To efficiently handle nonlinear constraints with parameter misspecification, we propose a single-loop inexact Augmented Lagrangian method that simultaneously updates the primal decision variables, dual multipliers, and the misspecified parameter. The method combines a forward-reflected-backward step with an Augmented Lagrangian penalty, and explicitly handles misspecification on both the operator and constraint functions. Moreover, we introduce a relaxed performance metric based on the Minty VI gap combined with an aggregated infeasibility metric. By proving boundedness of the dual iterates, we establish $\mathcal{O}(1/K)$ ergodic convergence rates for these metrics. Numerical Experiments are provided to showcase the superior performance of our algorithm compared to state-of-the-art methods.

  PublisherOA PDF

• On the Analysis of Misspecified Variational Inequalities with Nonlinear Constraints

  Zenodo (CERN European Organization for Nuclear Research) · 2026-03-20

  articleOpen accessSenior author

  In this paper, we study a class of misspecified variational inequalities (VIs) where both the monotone operator and nonlinear convex constraints depend on an unknown parameter learned via a secondary VI. Existing data-driven VI methods typically follow a decoupled learn-then-optimize scheme, causing the approximation error from the learning to propagate the main decision-making problem and hinder convergence. We instead consider a simultaneous approach that jointly solves the main and secondary VIs. To efficiently handle nonlinear constraints with parameter misspecification, we propose a single-loop inexact Augmented Lagrangian method that simultaneously updates the primal decision variables, dual multipliers, and the misspecified parameter. The method combines a forward-reflected-backward step with an Augmented Lagrangian penalty, and explicitly handles misspecification on both the operator and constraint functions. Moreover, we introduce a relaxed performance metric based on the Minty VI gap combined with an aggregated infeasibility metric. By proving boundedness of the dual iterates, we establish $\mathcal{O}(1/K)$ ergodic convergence rates for these metrics. Numerical experiments are provided to showcase the superior performance of our algorithm compared to state-of-the-art methods.

  PublisherDOI

• Variance-reduction for variational inequality problems with Bregman distance function

  Optimization methods & software · 2026-01-02

  articleSenior authorCorresponding
  PublisherDOI

• A Randomized Block-Coordinate Primal-Dual Method for Large-Scale Stochastic Saddle Point Problems

  INFORMS Journal on Optimization · 2026-02-25

  articleOpen access

  We consider (stochastic) convex-concave saddle point (SP) problems with high-dimensional decision variables, arising in various applications including machine learning problems. To contend with the challenges in computing full gradients, we employ a randomized block-coordinate primal-dual scheme in which randomly selected primal and dual blocks of variables are updated. We consider both deterministic and stochastic settings, where deterministic partial gradients and their randomly sampled estimates are used, respectively, at each iteration. We investigate the convergence of the proposed method under different blocking strategies and provide the corresponding complexity results. Although the best-known computational complexity result for computing a saddle point with [Formula: see text] primal-dual gap for deterministic primal-dual methods using full gradients is [Formula: see text], where m and n denote the dimensions of primal and dual variables, respectively, we show that our proposed randomized block-coordinate method achieves an improved complexity of [Formula: see text] assuming a coordinate-friendly structure on the problem. Moreover, for the stochastic setting where a mini-batch sample gradient is utilized, we show a computational complexity of [Formula: see text] through acceleration. Finally, almost sure convergence of the iterate sequence to a saddle point is established. Funding: N. Serhat Aybat was supported by the Office of Naval Research [Grant N00014-24-1-2666]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoo.2024.0056 .

  PublisherDOI

• Convergence analysis of non-strongly-monotone stochastic quasi-variational inequalities

  Optimization and Engineering · 2026-04-16

  preprintOpen accessSenior authorCorresponding
  PublisherOA PDFDOI

• On the Analysis of Misspecified Variational Inequalities with Nonlinear Constraints

  Open MIND · 2026-01-31

  preprintSenior author

  In this paper, we study a class of misspecified variational inequalities (VIs) where both the monotone operator and nonlinear convex constraints depend on an unknown parameter learned via a secondary VI. Existing data-driven VI methods typically follow a decoupled learn-then-optimize scheme, causing the approximation error from the learning to propagate the main decision-making problem and hinder convergence. We instead consider a simultaneous approach that jointly solves the main and secondary VIs. To efficiently handle nonlinear constraints with parameter misspecification, we propose a single-loop inexact Augmented Lagrangian method that simultaneously updates the primal decision variables, dual multipliers, and the misspecified parameter. The method combines a forward-reflected-backward step with an Augmented Lagrangian penalty, and explicitly handles misspecification on both the operator and constraint functions. Moreover, we introduce a relaxed performance metric based on the Minty VI gap combined with an aggregated infeasibility metric. By proving boundedness of the dual iterates, we establish $\mathcal{O}(1/K)$ ergodic convergence rates for these metrics. Numerical Experiments are provided to showcase the superior performance of our algorithm compared to state-of-the-art methods.

  DOI

• Semi-infinite Nonconvex Constrained Min-Max Optimization

  ArXiv.org · 2025-10-13

  preprintOpen access

  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.

  PublisherOA PDFDOI

• Distributionally Robust Nash Equilibria via Variational Inequalities

  ArXiv.org · 2025-10-19

  preprintOpen accessSenior author

  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.

  PublisherOA PDFDOI

• Riemannian Inexact Gradient Descent for Quadratic Discrimination

  ArXiv.org · 2025-07-07

  articleOpen accessSenior author

  We propose an inexact optimization algorithm on Riemannian manifolds, motivated by quadratic discrimination tasks in high-dimensional, low-sample-size (HDLSS) imaging settings. In such applications, gradient evaluations are often biased due to limited sample sizes. To address this, we introduce a novel Riemannian optimization algorithm that is robust to inexact gradient information and prove an $\mathcal O(1/K)$ convergence rate under standard assumptions. We also present a line search variant that requires access to function values but not exact gradients, maintaining the same convergence rate and ensuring sufficient descent. The algorithm is tailored to the Grassmann manifold by leveraging its geometric structure, and its convergence rate is validated numerically. A simulation of heteroscedastic images shows that when bias is introduced into the problem, both intentionally and through estimation of the covariance matrix, the detection performance of the algorithm solution is comparable to when true gradients are used in the optimization. The optimal subspace learned via the algorithm encodes interpretable patterns and shows qualitative similarity to known optimal solutions. By ensuring robust convergence and interpretability, our algorithm offers a compelling tool for manifold-based dimensionality reduction and discrimination in high-dimensional image data settings.

  PublisherOA PDF

Frequent coauthors

• Uday V. Shanbhag

  Pennsylvania State University

  16 shared

• Erfan Yazdandoost Hamedani

  14 shared

• Zeinab Alizadeh

  Shahid Sadoughi University of Medical Sciences and Health Services

  10 shared

• Farzad Yousefian

  7 shared

• Morteza Boroun

  University of Arizona

  5 shared

• Angelina Anani

  Rogers (United States)

  5 shared

• Ignacio Ortiz Flores

  5 shared

• Peter W. Glynn

  3 shared

Labs

• OPTIMA LabPI

Education

• PhD, Industrial and Manufacturing Engineering

  The Pennsylvania State University

  2020

Awards & honors

• Teacher of The Year College of Engineering, University of Ar…
• James E. Marley Graduate Fellowship in Engineering College o…
• Max and Joan Schlienger Graduate Scholarship College of Engi…
• Third Place winner in poster competition INFORMS, Fall 2018
• University Graduate Fellowship (UGF) The Pennsylvania State…