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Vietnam Journal of Mathematics 40:2&3(2012) 305-317

 

On Robust Multiobjective Optimization

Daishi Kuroiwa1 and Gue Myung Lee2

1Department of Mathematics, Shimane University, 1060, Nishikawatsu,

Matsue, Shimane 690-8504, Japan

2Department of Applied Mathematics, Pukyong National University,

Busan 608-737, Korea

Dedicated to Professor Phan Quoc Khanh on the occasion of his 65th birthday

Received December 5, 2011

Revised May 22, 2012

Abstract. The robust approach (the worst-case approach) for a multiobjective optimization problem (MP) with uncertainty data is considered. Using the robust approach, we define three kinds of robust efficient solutions for an uncertain multiobjective optimization problem (UMP) which consists of more than two objective functions with uncertainty data and constraint functions with uncertainty data. We give scalarizing methods for properly robust efficient solutions and weakly robust efficient solution of (UMP), and establish necessary optimality theorems for weakly and properly robust efficient solutions for (UMP).

2000 Mathematics Subject Classification. 90C29, 90C46.

Keywords. Robust multiobjective optimization, robust efficient solutions, scalarization, necessary optimality theorems.

 

 

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