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math.OC2023
On the Optimal Lower and Upper Complexity Bounds for a Class of Composite Optimization Problems
Zhenyuan Zhu, Fan Chen, Junyu Zhang +1
We study the optimal lower and upper complexity bounds for finding approximate solutions to the composite problem , where is smooth and is convex. Giv…
math.OC2022★ 1 cited
A Unified Primal-Dual Algorithm Framework for Inequality Constrained Problems
Zhenyuan Zhu, Fan Chen, Junyu Zhang +1
In this paper, we propose a unified primal-dual algorithm framework based on the augmented Lagrangian function for composite convex problems with conic inequality constraints. The…
math.OC2020★ 2 cited
Cubic Regularized Newton Method for Saddle Point Models: a Global and Local Convergence Analysis
Kevin Huang, Junyu Zhang, Shuzhong Zhang
In this paper, we propose a cubic regularized Newton (CRN) method for solving convex-concave saddle point problems (SPP). At each iteration, a cubic regularized saddle point subpro…