8 papers
Limiting Stationarity of Regularized Gap-Function Reformulations for Bilevel Optimization with Unbounded Multipliers
Xiaoning Bai, Shangzhi Zeng, Jin Zhang
Value-function-type reformulations have generated a broad class of methods for bilevel optimization. However, the corresponding value-function-type constraints are inherently degen…
Extended SQP Methods in Nonsmooth Difference Programming Applied to Problems with Variational Inequality Constraints
Boris S. Mordukhovich, Yixia Song, Shangzhi Zeng +1
This paper explores a new class of constrained difference programming problems, where the objective and constraints are formulated as differences of functions, without requiring th…
A Single-Loop Penalty-based Algorithm for Stochastic Minimax Optimization with Nonlinear Coupled Constraints
Qichao Cao, Shangzhi Zeng, Jin Zhang +1
We study stochastic nonconvex-concave minimax optimization with nonlinear coupled constraints that are convex in the maximization variable. To address the nonsmoothness arising fro…
A Single-Loop Bilevel Deep Learning Method for Optimal Control of Obstacle Problems
Yongcun Song, Shangzhi Zeng, Jin Zhang +1
Optimal control of obstacle problems arises in a wide range of applications and is computationally challenging due to its nonsmoothness, nonlinearity, and bilevel structure. Classi…
Alternating Gradient-Type Algorithm for Bilevel Optimization with Inexact Lower-Level Solutions via Moreau Envelope-based Reformulation
Xiaoning Bai, Shangzhi Zeng, Jin Zhang +1
In this paper, we study a class of bilevel optimization problems where the lower-level problem is a convex composite optimization model, which arises in various applications, inclu…
A Single-Loop Gradient Algorithm for Pessimistic Bilevel Optimization via Smooth Approximation
Qichao Cao, Shangzhi Zeng, Jin Zhang
Bilevel optimization has garnered significant attention in the machine learning community recently, particularly regarding the development of efficient numerical methods. While sub…