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Vietnam Journal of Mathematics 40:2&3(2012)
305-317
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On Robust Multiobjective Optimization
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Daishi Kuroiwa1 and Gue Myung
Lee2
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1Department
of Mathematics, Shimane University, 1060, Nishikawatsu,
Matsue, Shimane 690-8504, Japan
2Department
of Applied Mathematics, Pukyong National University,
Busan
608-737, Korea
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Dedicated to Professor
Phan Quoc Khanh on the occasion of his 65th birthday
Received December 5,
2011
Revised May 22, 2012
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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).
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2000 Mathematics
Subject Classification. 90C29, 90C46.
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Keywords.
Robust multiobjective optimization, robust efficient solutions,
scalarization, necessary optimality theorems.
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Established
by Vietnam Academy of Science and Technology &
Vietnam Mathematical Society
Published by
Springer since January 2013
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