On optimality conditions and duality theorems for robust semi-infinite multiobjective optimization problems

Jae Hyoung Lee () and Gue Myung Lee ()
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Jae Hyoung Lee: Pukyong National University
Gue Myung Lee: Pukyong National University

Annals of Operations Research, 2018, vol. 269, issue 1, No 20, 419-438

Abstract: Abstract In this paper, we consider a semi-infinite multiobjective optimization problem with more than two differentiable objective functions and uncertain constraint functions, which is called a robust semi-infinite multiobjective optimization problem and give its robust counterpart $${\mathrm{(RSIMP)}}$$ ( RSIMP ) of the problem, which is regarded as the worst case of the uncertain semi-infinite multiobjective optimization problem. We prove a necessary optimality theorem for a weakly robust efficient solution of $${\mathrm{(RSIMP)}} $$ ( RSIMP ) , and then give a sufficient optimality theorem for a weakly robust efficient solution of $${\mathrm{(RSIMP)}}$$ ( RSIMP ) . We formulate a Wolfe type dual problem of $${\mathrm{(RSIMP)}}$$ ( RSIMP ) and give duality results which hold between $${\mathrm{(RSIMP)}}$$ ( RSIMP ) and its dual problem.

Keywords: Semi-infinite programming; Multiobjective optimization; Robust optimization; Weakly robust efficient solution; Optimality conditions; Duality results; 90C29; 90C34; 90C46 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (9)

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DOI: 10.1007/s10479-016-2363-5

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