Componentwise versus global approaches to nonsmooth multiobjective optimization

Giancarlo Bigi

doi:10.3934/jimo.2005.1.21

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2005, Volume 1, Issue 1: 21-32. Doi: 10.3934/jimo.2005.1.21

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Componentwise versus global approaches to nonsmooth multiobjective optimization

Giancarlo Bigi^1,

1.
Dipartimento di Informatica, Università di Pisa, Largo B.Pontecorvo, 3, 56127 Pisa

Received: June 2004

Revised: December 2004

Published: January 2005

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Abstract

The paper aims to analyse and compare two different approaches to optimality conditions for multiobjective optimization problems, which involve nonsmooth functions. Both necessary and sufficient first order conditions are presented for the case in which constraint is given just as a set. Finally, the optimality conditions based on these two approaches are compared.

Keywords:

Dini¨CHadamard componentwise and set¨Cvalued derivatives,
generalized Jacobians,
tangent cones,
optimality conditions.

Mathematics Subject Classification: 90C46, 49J52, 90C29.

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