Optimality conditions and duality for nondifferentiable multiobjective programming

Optimality conditions and duality for nondifferentiable multiobjective programming

Xiaoyan GaoRuijie Wang 

College of Science, Xi'an University of Science and Technology, Xi'an 710054, China

Corresponding Author Email: 
https://doi.org/10.18280/rces.050202
Page: 
34-39
|
DOI: 
https://doi.org/10.18280/rces.050202
Received: 
10 December 2017
|
Accepted: 
16 June 2018
|
Published: 
30 June 2018
| Citation

OPEN ACCESS

Abstract: 

In this paper, we study a class of nonsmooth multiobjective optimization problem including inequality constraints. To the aim, some new functions named (pseudo, quasi) invex of order $\sigma(B, \varphi)-V-$ type II and strongly (quasi, pseudo) invex of order $\sigma(B, \varphi)-V-$ type II are introduced by using the tools of Clarke subdifferential. These new functions are used to derive and prove the sufficient optimality condition for a strict minimizer of the multiobjective programming problems. Moreover, the corresponding duality theorems are formulated for general Mond-Weir type dual program.

Keywords: 

optimality condition, duality, multiobje-ctive optimization problem

1. Introduction
2. Notations and Preliminaries
3. Optimality Condition
4. Mond-Weir Duality
5. Conclusions
Acknowledgment

This work is supported by Scientific Research Program Funded by Shaanxi Provincial Education Department (Program No. 15JK1456); Natural Science Foundation of shaanxi Province of China (Program No. 2017JM1041).

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