This paper studies the convex multiobjective optimization problem with vanishing constraints‎. ‎We introduce a new constraint qualification for these problems‎, ‎and then a necessary optimality condition for properly efficient solutions is presented‎. ‎Finally by imposing some assumptions‎, ‎we show that our necessary condition is also sufficient for proper efficiency‎. ‎Our results are formula...

In this paper we study a new optimality criterion, the K-optimality criterion, for constructing optimal experimental designs for polynomial regression models. We focus on the pth order polynomial regression model with symmetric design space [−1, 1]. For this model, we show that there is always a symmetric K-optimal design with exactly p + 1 support points including the boundary points −1 and 1....

One of the most important optimality conditions to aid in solving a vector optimization problem is the first-order necessary optimality condition that generalizes the Karush-Kuhn-Tucker condition. However, to obtain the sufficient optimality conditions, it is necessary to impose additional assumptions on the objective functions and on the constraint set.The present work is concerned with the co...

A new optimality condition for minimization with general constraints is introduced. Unlike the KKT conditions, this condition is satissed by local minimizers of nonlinear programming problems, independently of constraint qualiications. The new condition implies, and is strictly stronger than, Fritz-John optimality conditions. Suu-ciency for convex programming is proved.

In this paper, we establish global optimality conditions for quadratic optimization problems with quadratic equality and bivalent constraints. We first present a necessary and sufficient condition for a global minimizer of quadratic optimization problems with quadratic equality and bivalent constraints. Then, we examine situations where this optimality condition is equivalent to checking the po...