Proper andisolated efficiencies in multiobjective optimization problems - Thái, Doãn Chương (Trường Đại học Đà Lạt, 2012)
We employ some advanced tools of variational analysis and generalized differentiation such as the nonsmooth version of Fermat's rule, the limiting subdifferentia! of maximum functions, and the sum rules for the Frechet and Mordukhovich subdiHerentials to establish necessary conditions for (local) properly efficient solutions and (local) isolated minimizers of a multiobjective optimization problem involving inequality and equality constraints. Sufficient conditions for the existence of such solutions are also supplied under assumptions of (local) convex/affine functions or L-invex-infine functions defined in terms of the limiting subdifferential of locally Lipschitz functions. In addition, we propose a type of Wolfe dual problem and explore weak/strong duality relations under L-invexity-infineness hypotheses.Mathematics Subject Classification. 49J40, 49J53, 90C29.