Open AccessNECESSARY OPTIMALITY CONDITIONS FOR NONSMOOTH VECTOR OPTIMIZATION PROBLEMS
Author(s) -
Davide La Torre
Publication year - 2003
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.2003.9637221
Subject(s) - mathematics , subderivative , vector optimization , directional derivative , mathematical optimization , order (exchange) , derivative (finance) , vector valued function , optimization problem , pure mathematics , regular polygon , mathematical analysis , convex optimization , multi swarm optimization , geometry , finance , financial economics , economics
In this paper we introduce a notion of generalized derivative for nonsmooth vector functions in order to obtain necessary optimality conditions for vector optimization problems. This definition generalizes to the vector case the notion introduced by Michel and Penot and extended by Yang and Jeyakumar. This generalized derivative is contained in the Clarke subdifferential and then the corresponding optimality conditions are sharper than the Clarke's ones.