‎in this paper, using the idea of convexificators, we study boundedness and nonemptiness of lagrange multipliers satisfying the first order necessary conditions. we consider a class of nons- mooth fractional programming problems with equality, inequality constraints and an arbitrary set constraint. within this context, define generalized mangasarian-fromovitz constraint qualification and show t...

In this paper, a displacement-constrained volume-minimizing topology optimization model is present for two-dimensional continuum problems. The new model is a generalization of the displacement-constrained volume-minimizing model developed by Yi and Sui [1] in which the displacement is constrained in the loading point. In the original model the displacement constraint was formulated as an equali...

‎In this paper, using the idea of convexificators, we study boundedness and nonemptiness of Lagrange multipliers satisfying the first order necessary conditions. We consider a class of nons- mooth fractional programming problems with equality, inequality constraints and an arbitrary set constraint. Within this context, define generalized Mangasarian-Fromovitz constraint qualification and sh...

In recent years, sequential optimality conditions are frequently used for convergence of iterative methods to solve nonlinear constrained optimization problems. The sequential optimality conditions do not require any of the constraint qualications. In this paper, We present the necessary sequential complementary approximate Karush Kuhn Tucker (CAKKT) condition for a point to be a solution of a ...

 We consider generalized semi-infinite programming problems in which the index set of the inequality constraints depends on the decision vector and all emerging functions are assumed to be convex. Considering a lower level constraint qualification, we derive a formula for estimating the subdifferential of the value function. Finally, we establish the Fritz-John necessary optimality con...

A very general optimization problem with a variational inequality constraint, inequality constraints, and an abstract constraint are studied. Fritz John type and Kuhn–Tucker type necessary optimality conditions involving Mordukhovich coderivatives are derived. Several constraint qualifications for the Kuhn–Tucker type necessary optimality conditions involving Mordukhovich coderivatives are intr...

In this paper we study optimization problems with infinite many inequality constraints on a Banach space where the objective function and the binding constraints are Lipschitz near the optimal solution. Necessary optimality conditions and constraint qualifications in terms of Michel-Penot subdifferential are given.

In this paper we study the nonsmooth semi-infinite programming problem with inequality constraints. First, we consider the notions of local cone approximation $Lambda$ and $Lambda$-subdifferential. Then, we derive the Karush-Kuhn-Tucker optimality conditions under the Abadie and the Guignard constraint qualifications.

We consider the extended trust region subproblem (eTRS) as the minimization of an indefinite quadratic function subject to the intersection of unit ball with a single linear inequality constraint. Using a variation of the S-Lemma, we derive the necessary and sufficient optimality conditions for eTRS. Then, an OCP/SDP formulation is introduced for the problem. Finally, several illustrative examp...