E-optimality conditions and Wolfe E-duality for E-differentiable vector optimization problems with inequality and equality constraints
Tadeusz Antczak, Najeeb Abdulaleem · The Journal of Nonlinear Sciences and Applications · 2019
In this paper, a nonconvex vector optimization problem with both inequality and equality constraints is considered. The functions constituting it are not necessarily differentiable, but they are \(E\)-differentiable. The so-called \(E\)-Fritz John necessary optimality conditions and the so-called \(E\)-Karush-Kuhn-Tucker necessary optimality conditions are established for the considered \(E\)-differentiable multiobjective programming problems with both inequality and equality constraints. Further, the sufficient optimality conditions are derived for such nonconvex nonsmooth vector optimization problems under (generalized) \(E\)-convexity. The so-called vector \(E\)-Wolfe dual problem is defined for the considered \(E\)-differentiable multiobjective programming problem with both inequality and equality constraints and several dual theorems are established also under (generalized) \(E\)-convexity hypotheses.