Optimality conditions and a classification of duality schemes in vector optimization

• Autorzy: El Ghali B.
• Języki publikacji: EN

Abstrakty

EN

Vector minimization of a relation F valued in an ordered vector space under a constraint A consists in finding x[0] belongs to A, w[0] belongs to Fx[0] such that w[0] is minimal in FA. To a family of vector minimization problems minimize[x belongs to X] F(x, y), y [belongs to] Y, one associates a Lagrange relation [L(x, [xi], y[0]) = union of sets y belongs to Y(F(x, y)-xi(y)+(y[0]))] where [xi] belongs to an arbitrary class [Xi] of mappings. For this type of problem, there exist several notions of solutions. Some useful characterizations of existential solutions are established and, consequently, some necessary conditions of optimality are derived. One result of intermediate duality is proved with the aid of the scalarization theory. Existence theorems for existential solutions are given and a comparison of several exact duality schemes is established, more precisely in the convex case it is shown that the majority of exact duality schemes can be obtained from one result of S. Dolecki and C. Malivert.

Słowa kluczowe

EN

duality; existential solutions; minimality; vector optimization

PL

dwoistość; optymalizacja wektorowa

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2000
• Tom: Vol. 29, no 4
• Strony: 839--860
• Opis fizyczny: Bibliogr. 26 poz.,

Twórcy

autor

El Ghali B.