Scalarizations and Lagrange multipliers forapproximate solutions in the vector optimization problems withset-valued maps

Ying Gao; Xinmin Yang; Jin Yang; Hong Yan

doi:10.3934/jimo.2015.11.673

Article Contents

2015, Volume 11, Issue 2: 673-683. Doi: 10.3934/jimo.2015.11.673

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Scalarizations and Lagrange multipliers for approximate solutions in the vector optimization problems with set-valued maps

1.
Department of Mathematics, Chongqing Normal University, Chongqing 400047
2.
Department of Mathematics, Chongqing Normal University, Chongqing, 400047
3.
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong
4.
Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hong Kong

Received: August 2013

Revised: June 2014

Published: April 2015

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Abstract

In this paper, we characterize approximate solutions of vector optimization problems with set-valued maps. We gives several characterizations of generalized subconvexlike set-valued functions(see [10]), which is a generalization of nearly subconvexlike functions introduced in [34]. We present alternative theorem and derived scalarization theorems for approximate solutions with generalized subconvexlike set-valued maps. And then, Lagrange multiplier theorems under generalized Slater constraint qualification are established.

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

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