Work

A Lagrange function approach to study second-order optimality conditions for infinite-dimensional optimization problems

Year: 2025

Type: article

Abstract: In this paper, we focus on the second-order optimality conditions for infinite-dimensional optimization problems constrained by generalized polyhedral convex sets. Our aim is to further explore the role of the generalized polyhedral convex property, which is inspired by the findings of other authors. To this end, we employ the concept of Fréchet second-order subdifferential, a tool in variational analysis, to establish optimality conditions. Furthermore, by applying this concept to the Lagrangian function associated with the problem, we are able to derive refined optimality conditions that surpass existing results. The unique properties of generalized polyhedral convex sets play a crucial role in enabling these improvements.

Source: HPU2 Journal of Science Natural Sciences and Technology

DOI: 10.56764/hpu2.jos.2025.4.01.20-30

Authors: Duc-Tam Luong, Thu-Loan Vu Thi, Thi-Ngoan Dang

Institutions: Thai Nguyen University of Agriculture and Forestry, Phenikaa University

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funder: Bộ Giáo dục và Ðào tạo

Award: G7585048388