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Optimality criteria in set-valued optimization

Part of: Existence theories

Published online by Cambridge University Press:  09 April 2009

C. S. Lalitha ,
J. Dutta  and
Misha G. Govil
C. S. Lalitha
Affiliation:
Department of Mathematics Rajdhani CollegeRaja Garden New Delhi-110015, India
J. Dutta
Affiliation:
Department of Mathematics India Institute of TechnologyKanpur-208016India e-mail: jdutta@iitk.ac.in
Misha G. Govil
Affiliation:
Department of Mathematics Shri Ram College of Commerce University of DelhiDelhi-110007, India
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Abstract

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The main aim of this paper is to obtain optimality conditions for a constrained set-valued optimization problem. The concept of Clarke epiderivative is introduced and is used to derive necessary optimality conditions. In order to establish sufficient optimality criteria we introduce a new class of set-valued maps which extends the class of convex set-valued maps and is different from the class of invex set-valued maps.

Keywords

set-valued optimizationcontingent epiderivativeClarke epiderivativeconearcwise connectednessoptimality

MSC classification

Secondary: 49J53: Set-valued and variational analysis 90C30: Nonlinear programming
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 75 , Issue 2 , October 2003 , pp. 221 - 232
Copyright
Copyright © Australian Mathematical Society 2003

References

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