Optimality conditions of fenchel-lagrange duality and farkas-type results for composite dc infinite programs

Gang Li; Yinghong Xu; Zhenhua Qin

doi:10.3934/jimo.2021019

Article Contents

2022, Volume 18, Issue 2: 1275-1293. Doi: 10.3934/jimo.2021019

This issue Previous Article Solution method for discrete double obstacle problems based on a power penalty approach Next Article A globally convergent BFGS method for symmetric nonlinear equations

Optimality conditions of fenchel-lagrange duality and farkas-type results for composite dc infinite programs

1.
Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018, China
2.
Department of Information Technology, Zhejiang Institute of Mechanical & Electrical Engineering, Hangzhou 310053, China

^*Corresponding author
^*Corresponding author

Received: April 30, 2020

Revised: November 30, 2020

Early access: January 2021

Published: March 2022

This work was supported by the Natural Science Foundation of China (11401533), the Zhejiang Provincial Natural Science Foundation of China (LY18A010030), the Scientific Research Fund of Zhejiang Provincial Education Department (19060042-F) and the Science Foundation of Zhejiang Sci-Tech University (19062150-Y)

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Abstract

This paper is concerned with a DC composite programs with infinite DC inequalities constraints. Without any topological assumptions and generalized increasing property, we first construct some new regularity conditions by virtue of the epigraph technique. Then we give some complete characterizations of the (stable) Fenchel-Lagrange duality and the (stable) Farkas-type assertions. As applications, corresponding assertions for the DC programs with infinite inequality constraints and the conic programs with DC composite function are also given.

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Mathematics Subject Classification: Primary: 90C26, 90C30; Secondary: 90C46.

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