Work

Saddle Points of Partial Augmented Lagrangian Functions

Year: 2025

Type: article

Abstract: In this paper, we study a class of optimization problems with separable constraint structures, characterized by a combination of convex and nonconvex constraints. To handle these two distinct types of constraints, we introduce a partial augmented Lagrangian function by retaining nonconvex constraints while relaxing convex constraints into the objective function. Specifically, we employ the Moreau envelope for the convex term and apply second-order variational geometry to analyze the nonconvex term. For this partial augmented Lagrangian function, we study its saddle points and establish their relationship with KKT conditions. Furthermore, second-order optimality conditions are developed by employing tools such as second-order subdifferentials, asymptotic second-order tangent cones, and second-order tangent sets.

Source: Mathematical and Computational Applications

DOI: 10.3390/mca30050110

Authors: Longfei Huang, Jingyong Tang, Yutian Wang, Jinchuan Zhou

Institutions: Shandong University of Technology, Xinyang Normal University

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,689

Funders: National Natural Science Foundation of China, Natural Science Foundation of Shandong Province