Lagrange Duality and Saddle Point Optimality Conditions for Multiobjective Semi-Infinite Programming with Vanishing Constraints

Abstract

The objective of this paper is to investigate multiobjective semi-infinite programming problems with vanishing constraints (in brief, MSIPVC). We firstly propose both the vector Lagrange dual problems and the scalarized Lagrange dual problems for MSIPVC and explore duality relations under convexity assumptions. Then, the saddle point optimality conditions for MSIPVC are considered. Some examples are also given to illuminate the main results.

KEYWORDS:

• Multiobjective semi-infinite programming
• saddle point optimality conditions
• scalarized Lagrange dual problems
• vanishing constraints
• vector Lagrange dual problems

Acknowledgments

The authors would like to thank the Editors for the help in the processing of the article.

Additional information

Funding

This work was supported by The Ministry of Education and Training of Vietnam under Grant No. B2022-TCT-01.