About

Erfan Yazdandoost Hamedani is an Assistant Professor of Systems and Industrial Engineering at the University of Arizona. He received his PhD in Industrial Engineering and Operations Research from The Pennsylvania State University and holds a BSc degree in Mathematics and Applications from The University of Tehran. His research interests include distributed optimization, saddle point problems, bilevel optimization, machine learning, and data science. His work focuses on developing and analyzing algorithms for solving convex and non-convex large-scale optimization problems relevant to machine learning and data science. He has contributed to the field through various publications and presentations, emphasizing primal-dual methods, variance reduction, and large-scale optimization techniques.

Research topics

• Computer Security
• Computer Science
• Business
• Risk analysis (engineering)

Selected publications

• On the Analysis of Misspecified Variational Inequalities with Nonlinear Constraints

  ArXiv.org · 2026-01-31

  articleOpen access

  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

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

  INFORMS Journal on Optimization · 2026-02-25

  articleOpen access1st authorCorresponding

  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

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

  Optimization methods & software · 2026-01-02

  article
  PublisherDOI

• On the Analysis of Misspecified Variational Inequalities with Nonlinear Constraints

  Open MIND · 2026-01-31

  preprint

  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 accessSenior author

  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

• Safe Gradient Flow for Bilevel Optimization

  ArXiv.org · 2025-01-27

  preprintOpen access

  Bilevel optimization is a key framework in hierarchical decision-making, where one problem is embedded within the constraints of another. In this work, we propose a control-theoretic approach to solving bilevel optimization problems. Our method consists of two components: a gradient flow mechanism to minimize the upper-level objective and a safety filter to enforce the constraints imposed by the lower-level problem. Together, these components form a safe gradient flow that solves the bilevel problem in a single loop. To improve scalability with respect to the lower-level problem's dimensions, we introduce a relaxed formulation and design a compact variant of the safe gradient flow. This variant minimizes the upper-level objective while ensuring the lower-level decision variable remains within a user-defined suboptimality. Using Lyapunov analysis, we establish convergence guarantees for the dynamics, proving that they converge to a neighborhood of the optimal solution. Numerical experiments further validate the effectiveness of the proposed approaches. Our contributions provide both theoretical insights and practical tools for efficiently solving bilevel optimization problems.

  PublisherOA PDFDOI

• Sequential QCQP for Bilevel Optimization with Line Search

  ArXiv.org · 2025-05-20

  preprintOpen access

  Bilevel optimization involves a hierarchical structure where one problem is nested within another, leading to complex interdependencies between levels. We propose a single-loop, tuning-free algorithm that guarantees anytime feasibility, i.e., approximate satisfaction of the lower-level optimality condition, while ensuring descent of the upper-level objective. At each iteration, a convex quadratically-constrained quadratic program (QCQP) with a closed-form solution yields the search direction, followed by a backtracking line search inspired by control barrier functions to ensure safe, uniformly positive step sizes. The resulting method is scalable, requires no hyperparameter tuning, and converges under mild local regularity assumptions. We establish an O(1/k) ergodic convergence rate in terms of a first-order stationary metric and demonstrate the algorithm's effectiveness on representative bilevel tasks.

  PublisherOA PDFDOI

• Perturbed Gradient Descent via Convex Quadratic Approximation for Nonconvex Bilevel Optimization

  ArXiv.org · 2025-04-24

  preprintOpen accessSenior author

  Bilevel optimization is a fundamental tool in hierarchical decision-making and has been widely applied to machine learning tasks such as hyperparameter tuning, meta-learning, and continual learning. While significant progress has been made in bilevel optimization, existing methods predominantly focus on the {nonconvex-strongly convex, or the} nonconvex-PL settings, leaving the more general nonconvex-nonconvex framework underexplored. In this paper, we address this gap by developing an efficient gradient-based method inspired by the recently proposed Relaxed Gradient Flow (RXGF) framework with a continuous-time dynamic. In particular, we introduce a discretized variant of RXGF and formulate convex quadratic program subproblems with closed-form solutions. We provide a rigorous convergence analysis, demonstrating that under the existence of a KKT point and a regularity assumption {(lower-level gradient PL assumption)}, our method achieves an iteration complexity of $\mathcal{O}(1/ε^{1.5})$ in terms of the squared norm of the KKT residual for the reformulated problem. Moreover, even in the absence of the regularity assumption, we establish an iteration complexity of $\mathcal{O}(1/ε^{3})$ for the same metric. Through extensive numerical experiments on convex and nonconvex synthetic benchmarks and a hyper-data cleaning task, we illustrate the efficiency and scalability of our approach.

  PublisherOA PDFDOI

• On the Complexity of Finding Stationary Points in Nonconvex Simple Bilevel Optimization

  ArXiv.org · 2025-07-30

  preprintOpen access

  In this paper, we study the problem of solving a simple bilevel optimization problem, where the upper-level objective is minimized over the solution set of the lower-level problem. We focus on the general setting in which both the upper- and lower-level objectives are smooth but potentially nonconvex. Due to the absence of additional structural assumptions for the lower-level objective-such as convexity or the Polyak-Łojasiewicz (PL) condition-guaranteeing global optimality is generally intractable. Instead, we introduce a suitable notion of stationarity for this class of problems and aim to design a first-order algorithm that finds such stationary points in polynomial time. Intuitively, stationarity in this setting means the upper-level objective cannot be substantially improved locally without causing a larger deterioration in the lower-level objective. To this end, we show that a simple and implementable variant of the dynamic barrier gradient descent (DBGD) framework can effectively solve the considered nonconvex simple bilevel problems up to stationarity. Specifically, to reach an $(ε_f, ε_g)$-stationary point-where $ε_f$ and $ε_g$ denote the target stationarity accuracies for the upper- and lower-level objectives, respectively-the considered method achieves a complexity of $\mathcal{O}\left(\max\left(ε_f^{-\frac{3+p}{1+p}}, ε_g^{-\frac{3+p}{2}}\right)\right)$, where $p \geq 0$ is an arbitrary constant balancing the terms. To the best of our knowledge, this is the first complexity result for a discrete-time algorithm that guarantees joint stationarity for both levels in general nonconvex simple bilevel problems.

  PublisherOA PDFDOI

• Safe Gradient Flow for Bilevel Optimization

  2025-07-08 · 1 citations

  article

  Bilevel optimization is a key framework in hierarchical decision-making, where one problem is embedded within the constraints of another. In this work, we propose a control-theoretic approach to solving bilevel optimization problems. Our method consists of two components: a gradient flow mechanism to minimize the upper-level objective and a safety filter to enforce the constraints imposed by the lower-level problem. Together, these components form a safe gradient flow that solves the bilevel problem in a single loop. To improve scalability with respect to the lower-level problem’s dimensions, we introduce a relaxed formulation and design a compact variant of the safe gradient flow. This variant minimizes the upper-level objective while ensuring the lower-level decision variable remains within a user-defined suboptimality. Using Lyapunov analysis, we establish convergence guarantees for the dynamics, proving that they converge to a neighborhood of the optimal solution. Numerical experiments further validate the effectiveness of the proposed approaches. Our contributions provide both theoretical insights and practical tools for efficiently solving bilevel optimization problems.

  PublisherDOI

Recent grants

• Collaborative Research: Computationally Efficient Algorithms for Large-scale Bilevel Optimization Problems

  NSF · $224k · 2021–2024

Frequent coauthors

• Necdet Serhat Aybat

  Pennsylvania State University

  21 shared

• Afrooz Jalilzadeh

  University of Arizona

  14 shared

• Nazanin Abolfazli

  University of Arizona

  6 shared

• Aryan Mokhtari

  5 shared

• Ruichen Jiang

  5 shared

• Md Habibor Rahman

  University of Arizona

  2 shared

• Jincheng Cao

  2 shared

• Young-Jun Son

  Purdue University West Lafayette

  2 shared

Labs

• Erfan Yazdandoost Hamedani LabPI

Education

• PhD in Industrial Engineering and Operations Research, Industrial and Manufacturing Engineering

  Pennsylvania State University

  2020