An approximate strong KKT condition for multiobjective optimization

Min Feng () and Shengjie Li ()
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Min Feng: Chongqing University
Shengjie Li: Chongqing University

TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, 2018, vol. 26, issue 3, No 10, 489-509

Abstract: Abstract In this paper, we introduce a sequential approximate strong Karush–Kuhn–Tucker (ASKKT) condition for a multiobjective optimization problem with inequality constraints. We show that each local efficient solution satisfies the ASKKT condition, but weakly efficient solutions may not satisfy it. Subsequently, we use a so-called cone-continuity regularity (CCR) condition to guarantee that the limit of an ASKKT sequence converges to an SKKT point. Finally, under the appropriate assumptions, we show that the ASKKT condition is also a sufficient condition of properly efficient points for convex multiobjective optimization problems.

Keywords: Multiobjective optimization; Strong KKT conditions; Approximate KKT conditions; Regularity conditions; Properly efficient solutions; 90C29; 90C46 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s11750-018-0491-6

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