About

Shuzhong Zhang is a Professor and founding Department Head of the Department of Industrial and System Engineering at the University of Minnesota. He received a B.Sc. in Applied Mathematics from Fudan University in 1984 and a Ph.D. in Operations Research and Econometrics from the Tinbergen Institute, Erasmus University, in 1991. His professional background includes faculty positions at the Department of Econometrics at the University of Groningen, the Econometric Institute at Erasmus University, and the Department of Systems Engineering & Engineering Management at The Chinese University of Hong Kong, where he served as a Professor. Since 2011, he has been a faculty member at the University of Minnesota, serving as the founding Department Head from 2012 to 2018. His research interests encompass decision models within Operations Research, optimization, machine learning, and statistical learning, with activities spanning modeling, algorithm design, theory, and applications in these areas. Dr. Zhang has received numerous awards for his research and teaching, including the Erasmus University Research Prize, the SIAM Outstanding Paper Prize, and the IEEE Signal Processing Society Best Paper Award. He has served on editorial boards of prominent journals such as Operations Research and Management Science and has been actively involved in professional societies including INFORMS, SIAM, and MOS.

Research topics

• Biology
• Immunology
• Cell biology
• Cancer research
• Medicine
• Internal medicine

Selected publications

• An Approximation-Based Regularized Extra-Gradient Method for Monotone Variational Inequalities

  SIAM Journal on Optimization · 2025-07-03 · 1 citations

  articleSenior author
  PublisherDOI

• ENaC contributes to macrophage dysfunction in cystic fibrosis

  American Journal of Physiology-Lung Cellular and Molecular Physiology · 2025-06-02 · 2 citations

  articleOpen access

  New research reveals that epithelial sodium channel (ENaC) overexpression in cystic fibrosis (CF) immune cells impairs macrophage function. Inhibiting ENaC increases cystic fibrosis transmembrane conductance regulator (CFTR) expression, normalizes reactive oxygen species production, improves autophagy, and reduces proinflammatory cytokine production. This suggests that ENaC modulation could be a novel therapeutic target for CF infection control, either alone or with CFTR modulators, offering new hope for patients not eligible for current treatments.

  PublisherDOI

• A Unified Analysis on the Subgradient Upper Bounds for the Subgradient Methods Minimizing Composite Nonconvex, Nonsmooth, and Non-Lipschitz Functions

  Journal of the Operations Research Society of China · 2025-12-16

  articleSenior author
  PublisherDOI

• Complexity Analysis of Convex Majorization Schemes for Nonconvex Constrained Optimization

  ArXiv.org · 2025-06-10

  preprintOpen accessSenior author

  We introduce and study various algorithms for solving nonconvex minimization with inequality constraints, based on the construction of convex surrogate envelopes that majorize the objective and the constraints. In the case where the objective and constraint functions are gradient Hölderian continuous, the surrogate functions can be readily constructed and the solution method can be efficiently implemented. The surrogate envelopes are extended to the settings where the second-order information is available, and the convex subproblems are further represented by Dikin ellipsoids using the self-concordance of the convex surrogate constraints. Iteration complexities have been developed for both convex and nonconvex optimization models. The numerical results show promising potential of the proposed approaches.

  PublisherOA PDFDOI

• A Correspondence-Driven Approach for Bilevel Decision-making with Nonconvex Lower-Level Problems

  arXiv (Cornell University) · 2025-09-01

  preprintOpen accessSenior author

  We consider bilevel optimization problems with general nonconvex lower-level objectives and show that the classical hyperfunction-based formulation is unsettled, since the global minimizer of the lower-level problem is generally unattainable. To address this issue, we propose a correspondence-driven hyperfunction $ϕ^{\text{cd}}$. In this formulation, the follower is modeled not as a rational agent always attaining a global minimizer, but as an algorithm-based bounded rational agent whose decisions are produced by a fixed algorithm with initialization and step size. Since $ϕ^{\text{cd}}$ is generally discontinuous, we apply Gaussian smoothing to obtain a smooth approximation $ϕ^{\text{cd}}_ξ$, then show that its value and gradient converge to those of $ϕ^{\text{cd}}$. In the nonconvex setting, we identify that bifurcation phenomena, which arise when $g(x,\cdot)$ has a degenerate stationary point, pose a key challenge for hyperfunction-based methods. This is especially the case when $ϕ^{\text{cd}}_ξ$ is solved using gradient methods. To overcome this challenge, we analyze the geometric structure of the bifurcation set under some weak assumptions. Building on these results, we design a biased projected SGD-based algorithm SCiNBiO to solve $ϕ^{\text{cd}}_ξ$ with a cubic-regularized Newton lower-level solver. We also provide convergence guarantees and oracle complexity bounds for the upper level. Finally, we connect bifurcation theory from dynamical systems to the bilevel setting and define the notion of fold bifurcation points in this setting. Under the assumption that all degenerate stationary points are fold bifurcation points, we establish the oracle complexity of SCiNBiO for the lower-level problem.

  PublisherOA PDFDOI

• New Classes of Non-monotone Variational Inequality Problems Solvable via Proximal Gradient on Smooth Gap Functions

  ArXiv.org · 2025-10-14

  preprintOpen accessSenior author

  In this paper, we study the local linear convergence behavior of proximal-gradient (PG) descent algorithm on a parameterized gap-function reformulation of a smooth but non-monotone variational inequality problem (VIP). The aim is to solve the non-monotone VI problem without assuming the existence of a Minty-type solution. We first introduce and study various error bound conditions for the gap functions in relation to the VI model. In particular, we show that uniform type error bounds imply level-set type error bounds for composite optimization, revealing a key hierarchical structure there. As a result, local linear convergence is established under some easy-verifiable conditions induced by level-set error bounds, the gradient Lipschitz condition and a suitable initialization condition. Furthermore, for non-monotone affine VIs we present a homotopy continuation scheme that achieves global convergence by dynamically tracing a solution path. Our numerical experiments show the efficacy of the proposed approach, leading to the solutions of a broad class of non-monotone VI problems resulting from the need to compute Nash equilibria, traffic controls, and the GAN models.

  PublisherOA PDFDOI

• New Results on the Polyak Stepsize: Tight Convergence Analysis and Universal Function Classes

  arXiv (Cornell University) · 2025-12-06

  preprintOpen accessSenior author

  In this paper, we revisit a classical adaptive stepsize strategy for gradient descent: the Polyak stepsize (PolyakGD), originally proposed in Polyak (1969). We study the convergence behavior of PolyakGD from two perspectives: tight worst-case analysis and universality across function classes. As our first main result, we establish the tightness of the known convergence rates of PolyakGD by explicitly constructing worst-case functions. In particular, we show that the $O((1-\frac{1}κ)^K)$ rate for smooth strongly convex functions and the $O(1/K)$ rate for smooth convex functions are both tight. Moreover, we theoretically show that PolyakGD automatically exploits floating-point errors to escape the worst-case behavior. Our second main result provides new convergence guarantees for PolyakGD under both Hölder smoothness and Hölder growth conditions. These findings show that the Polyak stepsize is universal, automatically adapting to various function classes without requiring prior knowledge of problem parameters.

  PublisherOA PDFDOI

• Convergence analysis of the transformed gradient projection algorithms on compact matrix manifolds

  arXiv (Cornell University) · 2024-04-30

  preprintOpen accessSenior author

  In this paper, we study the optimization problem on a compact matrix manifold. While existing feasible algorithms can be broadly categorized into retraction-based and projection-based methods, compared to the more comprehensive and in-depth algorithmic and convergence research framework for retraction-based line-search (RetrLS) algorithms using only tangent vectors, the theoretical understanding and algorithmic design of projection-based line-search (ProjLS) algorithms remain limited, especially when general search directions and stepsizes are involved. To bridge this gap, we propose a unified algorithmic framework called the Transformed Gradient Projection (TGP) algorithm. The key idea is to construct the search direction as a transformed Riemannian (or Euclidean) gradient augmented by an additional normal component, allowing the framework to encompass and generalize numerous existing algorithms. Then, we conduct a thorough exploration of the convergence properties of the TGP algorithms under various stepsizes, including the Armijo, Zhang-Hager type nonmonotone Armijo, and fixed stepsizes. To achieve this, we extensively analyze the geometric properties of the projection onto compact matrix manifolds, which may be of independent interest. Building upon these insights, we establish the weak convergence, iteration complexity, and global convergence of TGP algorithms under three distinct stepsizes. In cases where the compact matrix manifold is the Stiefel or Grassmann manifold, our convergence results either encompass or surpass those found in the literature. Finally, through a series of numerical experiments and theoretical analysis, we observe that different choices of scaling matrices and normal components in the search direction of TGP algorithms can lead to significantly different performance in practice.

  PublisherOA PDFDOI

• A Barrier Function Approach for Bilevel Optimization with Coupled Lower-Level Constraints: Formulation, Approximation and Algorithms

  arXiv (Cornell University) · 2024-10-14

  preprintOpen accessSenior author

  In this paper, we consider bilevel optimization problem where the lower-level has coupled constraints, i.e. the constraints depend both on the upper- and lower-level variables. In particular, we consider two settings for the lower-level problem. The first is when the objective is strongly convex and the constraints are convex with respect to the lower-level variable; The second is when the lower-level is a linear program. We propose to utilize a barrier function reformulation to translate the problem into an unconstrained problem. By developing a series of new techniques, we proved that both the hyperfunction value and hypergradient of the barrier reformulated problem (uniformly) converge to those of the original problem under minimal assumptions. Further, to overcome the non-Lipschitz smoothness of hyperfunction and lower-level problem for barrier reformulated problems, we design an adaptive algorithm that ensures a non-asymptotic convergence guarantee. We also design an algorithm that converges to the stationary point of the original problem asymptotically under certain assumptions. The proposed algorithms require minimal assumptions, and to our knowledge, they are the first with convergence guarantees when the lower-level problem is a linear program. Numerical experiments are conducted to show the effectiveness of the proposed method.

  PublisherOA PDFDOI

• General Constrained Matrix Optimization

  arXiv (Cornell University) · 2024-10-13

  preprintOpen accessSenior author

  This paper presents and analyzes the first matrix optimization model which allows general coordinate and spectral constraints. The breadth of problems our model covers is exemplified by a lengthy list of examples from the literature, including semidefinite programming, matrix completion, and quadratically constrained quadratic programs (QCQPs), and we demonstrate our model enables completely novel formulations of numerous problems. Our solution methodology leverages matrix factorization and constrained manifold optimization to develop an equivalent reformulation of our general matrix optimization model for which we design a feasible, first-order algorithm. We prove our algorithm converges to $(ε,ε)$-approximate first-order KKT points of our reformulation in $\mathcal{O}(1/ε^2)$ iterations. The method we developed applies to a special class of constrained manifold optimization problems and is one of the first which generates a sequence of feasible points which converges to a KKT point. We validate our model and method through numerical experimentation. Our first experiment presents a generalized version of semidefinite programming which allows novel eigenvalue constraints, and our second numerical experiment compares our method to the classical semidefinite relaxation approach for solving QCQPs. For the QCQP numerical experiments, we demonstrate our method is able to dominate the classical state-of-the-art approach, solving more than ten times as many problems compared to the standard solution procedure.

  PublisherOA PDFDOI

Recent grants

• Polynomial Optimization: Solution Methods and Applications

  NSF · $360k · 2012–2015

• Gradient Methods for Solving Big Data (Tensor) Optimization Problems

  NSF · $300k · 2015–2019

Frequent coauthors

• J.F. Sturm

  Tilburg University

  35 shared

• Bo Jiang

  35 shared

• Shiqian Ma

  Rice University

  34 shared

• Simai He

  Jilin Normal University

  26 shared

• Yongwei Huang

  Guangdong University of Technology

  26 shared

• Zhening Li

  University of Portsmouth

  24 shared

• Zhi‐Quan Luo

  23 shared

• Tianyi Lin

  Columbia University

  22 shared

Education

• Ph.D., Tinbergen Institute

  Erasmus Universiteit Rotterdam

  1991

• BS, Mathematics

  Fudan University

  1984

Awards & honors

• Erasmus University Research Prize (1999)
• CUHK Vice-Chancellor Exemplary Teaching Award (2001)
• SIAM Outstanding Paper Prize (2003)
• IEEE Signal Processing Society Best Paper Award (2010)
• 2015 SPS Signal Processing Magazine Best Paper Award