On directionally differentiable multiobjective programming problems with vanishing constraints
研究了带不等式、等式和消失约束的方向可微多目标规划问题，在约束规格下建立了KKT型必要和充分最优性条件，并定义了向量Wolfe对偶问题证明了相关对偶定理。
Abstract In this paper, a class of directionally differentiable multiobjective programming problems with inequality, equality and vanishing constraints is considered. Under both the Abadie constraint qualification and the modified Abadie constraint qualification, the Karush–Kuhn–Tucker type necessary optimality conditions are established for such nondifferentiable vector optimization problems by using the nonlinear version Gordan theorem of the alternative for convex functions. Further, the sufficient optimality conditions for such directionally differentiable multiobjective programming problems with vanishing constraints are proved under convexity hypotheses. Furthermore, vector Wolfe dual problem is defined for the considered directionally differentiable multiobjective programming problem vanishing constraints and several duality theorems are established also under appropriate convexity hypotheses.