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S-strictly quasi-concave vector maximisation

Published online by Cambridge University Press:  17 April 2009

Hong-Bin Dong ,
Xun-Hua Gong ,
Shou-Yang Wang  and
Luis Coladas
Hong-Bin Dong
Affiliation:
Institute of Systems Science, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, China, e-mail: [email protected]
Xun-Hua Gong
Affiliation:
Department of Mathematics, Nanchang University, Nanchang 330047, China e-mail: [email protected]
Shou-Yang Wang
Affiliation:
Institute of Systems Science, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, China e-mail: [email protected] of Business Administration, Hunan University, Changsha, Hunan 410082, China e-mail: [email protected]
Luis Coladas
Affiliation:
Department of Statistics and Operations Research, Universidade de Santiago, 15782 Santiago de Compostela, Spain, e-mail: [email protected]
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Abstract

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In this paper, we discuss the relationship among the concepts of an S-strictly quasiconcave vector-valued function introduced by Benson and Sun, a C-strongly quasiconcave vector-valued function and a C-strictly quasiconcave vector-valued function in a topological vector space with a lattice ordering. We generalize a main result obtained by Benson and Sun about the closedness of an efficient solution set in multiple objective programming. We prove that an efficient solution set is closed and connected when the objective function is a continuous S-strictly quasiconcave vector-valued function, the objective space is a topological vector lattice and the ordering cone has a nonempty interior.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 67 , Issue 3 , June 2003 , pp. 429 - 443
Copyright
Copyright © Australian Mathematical Society 2003

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