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Optimality conditions for multiobjecttve and nonsmooth minimisation in abstract spaces

Published online by Cambridge University Press:  17 April 2009

L. Coladas ,
Z. Li  and
S. Wang
L. Coladas
Affiliation:
Departamento de Estadística eInvestigación Operativa Universidadde Santiago de Compostela 15771 Santiago de CompostelaSpain
Z. Li
Affiliation:
Institute of Systems Science AcademiaSinica Beijing 100080China
S. Wang
Affiliation:
Department of MathematicsUniversity of Inner MongoliaHohhot 010021China
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Abstract

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In this paper we study optimality conditions for an efficient solution in various senses of a general multiobjective optimisation problem in abstract spaces. We utilise properties of the Clarke's generalised differential and properties of a conesubconvexlike function to derive a few necessary and/or sufficient conditions for a feasible solution to be a weak minimum (a minimum, a strong minimum or a proper minimum) of the vector optimisation problem. The results in this paper are extensions and refinements of some known results in vector optimisation.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 50 , Issue 2 , October 1994 , pp. 205 - 218
Copyright
Copyright © Australian Mathematical Society 1994

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