Mathematical Modelling and Analysis (Jun 2003)

Necessary optimality conditions for nonsmooth vector optimization problems

  • Davide La Torre

DOI
https://doi.org/10.3846/13926292.2003.9637221
Journal volume & issue
Vol. 8, no. 2

Abstract

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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. Būtinos neglodžių vektorių optimizavimo uždavinių optimalios sąlygos Santrauka Straipsnyje ivedama apibendrintos išvestines savoka neglodžioms vektor‐funkcijoms, kad galima būtu gauti optimalumo salygas vektoriu optimizavimo uždaviniams. Šis apibrežimas apibendrina Michel ir Penot ivestas savokas, kurias išplete Yang ir Jeyakumar. Išvestines apibendrinimas ieina i Clarke subdiferenciala, tačiau optimalumo salygos yra jautresnes nei Clarko. First Published Online: 14 Oct 2010

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