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Lipschitz and differentiable dependence of solutions on a parameter in a scalarization method

Published online by Cambridge University Press:  09 April 2009

Alicia Sterna-Karwat
Alicia Sterna-Karwat
Affiliation:
Department of MathematicsMonash UniversityClayton, Victoria 3168, Australia
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Abstract

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This paper is concerned with a vector optimization problem set in a normed space where optimality is defined through a convex cone. The vector problem can be solved using a parametrized scalar problem. Under some convexity assumptions, it is shown that dependence of optimal solutions on the parameter is Lipschitz continuous. Hence differentiable dependence on the solutions on the parameter is derived.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 42 , Issue 3 , June 1987 , pp. 353 - 364
Copyright
Copyright © Australian Mathematical Society 1987

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