In this paper we give necessary optimality conditions of Fritz-John and Kuhn-Tucker (KKT) conditions for non-linear infinite dimensional programming problem with operatorial constraints. We use an alternative theorem. Some of the known results in finite dimensional case have been extended to infinite dimensional case with suitable conditions.

In this paper, we are concerned with a fractional multiobjective optimization problem ( P ). Using support functions together generalized Guignard constraint qualification, give necessary optimality conditions in terms of convexificators and the Karush–Kuhn–Tucker multipliers. Several intermediate problems have been introduced to help us our investigation.

This paper deals with optimality conditions to solve nonlinear programming problems. The classical Karush-Kuhn-Tucker (KKT) optimality conditions are demonstrated through a cone approach, using the well known Farkas’ Lemma. These conditions are valid at a minimizer of a nonlinear programming problem if a constraint qualification is satisfied. First we prove the KKT theorem supposing the equalit...

Support vector machines with ramp loss ( $$L_r$$ -SVM) have attracted considerable attention due to the robustness of loss. However, corresponding optimization problem is non-convex, and given Karush–Kuhn–Tucker (KKT) conditions are only first-order necessary conditions. To enrich optimality theory -SVM, we first introduce analyze proximal operator for loss, then establish a stronger condition:...

The bilevel program is a sequence of two optimization problems where the constraint region of the upper level problem is determined implicitly by the solution set to the lower level problem. The classical approach to solving such a problem is to replace the lower level problem by its Karush–Kuhn–Tucker (KKT) condition and solve the resulting mathematical programming problem with equilibrium con...

The stabilized version of the sequential quadratic programming algorithm (sSQP) had been developed in order to achieve fast convergence despite possible degeneracy of constraints of optimization problems, when the Lagrange multipliers associated to a solution are not unique. Superlinear convergence of sSQP had been previously established under the strong second-order sufficient condition for op...

Abstract This paper deals with a robust multiobjective optimization problem involving nonsmooth/nonconvex real-valued functions. Under an appropriate constraint qualification, we establish necessary optimality conditions for weakly efficient solutions of the considered problem. These are presented in terms Karush-Kuhn-Tucker multipliers and convexificators related Examples illustrating our find...

We consider a nonsmooth semi-infinite interval-valued vector programming problem, where the objectives and constraint functions need not to be locally Lipschitz. Using Abadie’s qualification convexificators, we provide Karush–Kuhn–Tucker necessary optimality conditions by converting initial problem into bi-criteria optimization problem. Furthermore, establish sufficient under asymptotic convexi...

This paper is devoted to provide sufficient Karush Kuhn Tucker (in short, KKT) conditions of optimality second-order for a set-valued fractional minimax problem. In addition, we define duals the types Mond-Weir and Wolfe Further obtain theorems duality under contingent epi-derivative together with generalized cone convexity suppositions second-order.

In this paper, by considering the parametric technique, we study a class of fractional optimization problems involving data uncertainty in objective functional. We formulate and prove robust Karush-Kuhn-Tucker necessary optimality conditions provide their sufficiency convexity and/or concavity assumptions involved functionals. addition, to complete study, an illustrative example is presented.