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 įvedama apibendrintos išvestinės sąvoka neglodžioms vektor‐funkcijoms, kad galima būtų gauti optimalumo sąlygas vektorių optimizavimo uždaviniams. Šis apibrėžimas apibendrina Michel ir Penot įvestas sąvokas, kurias išplėtė Yang ir Jeyakumar. Išvestinės apibendrinimas įeina į Clarke subdiferencialą, tačiau optimalumo sąlygos yra jautresnės nei Clarko.
La Torre, D. (2003). Necessary optimality conditions for nonsmooth vector optimization problems. Mathematical Modelling and Analysis, 8(2), 165-174. https://doi.org/10.3846/13926292.2003.9637221
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