Lagrangian Multipliers for Presubconvexlike Optimization Problems of Set Valued Functions
Renying Zeng
TL;DR
This paper explores the use of scalar and vector Lagrangian multipliers in constrained set-valued optimization, establishing conditions for the existence of weakly efficient solutions.
Contribution
It introduces new necessary and sufficient conditions for solutions in set-valued optimization problems using Lagrangian multipliers.
Findings
Derived necessary conditions for weakly efficient solutions.
Established sufficient conditions for solution existence.
Provided combined necessary and sufficient conditions.
Abstract
In this paper, we discuss scalar Lagrangian multipliers and vector Lagrangian multipliers for constrained set-valued optimization problems. We obtain some necessary conditions, sufficient conditions, as well as necessary and sufficient conditions for the existence of weakly efficient solutions.
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Taxonomy
TopicsOptimization and Variational Analysis · Advanced Optimization Algorithms Research · Fixed Point Theorems Analysis