Optimality criteria form the foundations of mathematical programming both theoretically and computationally. In general, these criteria can be classified as either necessary or sufficient. Of course, one would like to have the same criterion be both necessary and sufficient. However, this occurs only under somewhat ideal conditions which are rarely satisfied in practice. In the absence of conve...

This paper is concerned with the study of necessary and sufficient optimality conditions for convex–concave generalized fractional disjunctive programming problems for which the decision set is the union of a family of convex sets. The Lagrangian function for such problems is defined and the Kuhn–Tucker Saddle and Stationary points are characterized. In addition, some important theorems related...

When studying the information leakage in programs or protocols, a natural question arises: “what is the worst case scenario?”. This problem of identifying the maximal leakage can be seen as a channel capacity problem in the information theoretical sense. In this paper, by combining two powerful theories: Information Theory and Karush–Kuhn–Tucker conditions, we demonstrate a very general solutio...

We establish an abstract infinite dimensional KAM theorem dealing with unbounded perturbation vector-field, which could be applied to a large class of Hamiltonian PDEs containing the derivative ∂x in the perturbation. Especially, in this range of application lie a class of derivative nonlinear Schrödinger equations with Dirichlet boundary conditions and perturbed Benjamin-Ono equation with peri...

Stability properties of the problem of minimizing a (nonconvex) linear-quadratic function over an Euclidean ball, known as the trust-region subproblem, are studied in this paper. We investigate in detail the case where the linear part of the objective function is perturbed and obtain necessary and sufficient conditions for the upper/lower semicontinuity of the Karush-Kuhn-Tucker point set map a...

in this paper, a model of an optimal control problem with chance constraints is introduced. the parametersof the constraints are fuzzy, random or fuzzy random variables. todefuzzify the constraints, we consider possibility levels.  bychance-constrained programming the chance constraints are converted to crisp constraints which are neither fuzzy nor stochastic and then the resulting classical op...

Sequential optimality conditions for constrained optimization are necessarily satisfied by local minimizers, independently of the fulfillment of constraint qualifications. These conditions support the employment of different stopping criteria for practical optimization algorithms. On the other hand, when an appropriate strict constraint qualification associated with some sequential optimality c...

In this paper we obtain secondand first-order optimality conditions of Kuhn-Tucker type and Fritz John one for weak efficiency in the vector problem with inequality constraints. In the necessary conditions we suppose that the objective function and the active constraints are continuously differentiable. We introduce notions of KTSP-invex problem and second-order KTSP-invex one. We obtain that t...