# Lagrangian Multipliers for Presubconvexlike Optimization Problems of Set Valued Functions

## 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.

## Key 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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Source: https://tomesphere.com/paper/1706.03728