Optimality conditions for approximate solutions ofvector optimization problems

Ying Gao; Xinmin Yang; Kok Lay Teo

doi:10.3934/jimo.2011.7.483

Article Contents

2011, Volume 7, Issue 2: 483-496. Doi: 10.3934/jimo.2011.7.483

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Optimality conditions for approximate solutions of vector optimization problems

1.
Department of Mathematics, Chongqing Normal University, Chongqing 400047
2.
Department of Mathematics and Statistics, Curtin University, G.P.O. Box U1987, Perth, WA 6845

Received: September 30, 2009

Revised: February 28, 2011

Published: March 2011

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Abstract

In this paper, we introduce a new kind of properly approximate efficient solution of vector optimization problems. Some properties for this new class of approximate solutions are established. Also necessary and sufficient conditions via nonlinear scalarizations are obtained for properly approximate solutions. And under the assumption of cone subconvexlike functions, we derive linear scalarizations for properly approximate efficient solutions.

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Mathematics Subject Classification: 90C29, 90C30, 90C46.

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