We consider Karush-Kuhn-Tucker (KKT) systems, which depend on a parameter. Our contribution concerns with the existence of solution of the directionally perturbed KKT system, approximating the given primaldual base solution. To our knowledge, we give the first explicit result of this kind in the situation where the multiplier associated with the base primal solution may not be unique. The condi...

We consider an optimal control problem governed by an ODE with memory playing the role of a control. We show the existence of an optimal solution and derive some necessary optimality conditions. Some examples are then discussed.

In this paper we study a class of Mayer-type hybrid optimal control problems. Using Lagrange techniques, we formulate a version of the Hybrid Maximum Principle for optimal control problems governed by hybrid systems with autonomous location transitions in the presence of additional target constraints.

The cones of directions of constancy are used to derive: new as well as known optimality conditions; weakest constraint qualifications; and regularization techniques, for the convex programming problem. In addition, the "badly behaved set" of constraints, i.e. the set of constraints which causes problems in the Kuhn-Tucker theory, is isolated and a computational procedure for checking whether a...

In this article, we study the existence of solution for the following elliptic system of variable exponents with perturbation terms − div |∇u|p(x)−2∇u) + |u|p(x)−2u = λa(x)|u|γ(x)−2u+ Fu(x, u, v) in R , − div |∇v|q(x)−2∇v) + |v|q(x)−2v = λb(x)|v|δ(x)−2v + Fv(x, u, v) in R , u ∈W 1,p(·)(RN ), v ∈W 1,q(·)(RN ), where the corresponding functional does not satisfy PS conditions. We obtain a suffici...

In this paper we discuss second-order properties of the Moreau-Yosida regularization F of a piecewise twice continuously differentiable convex function f . We introduce a new constraint qualification in order to prove that the gradient of F is piecewise continuously differentiable. In addition, we discuss conditions, depending on the Hessians of the pieces, that guarantee positive definiteness ...

The mechanical rolling conditions in hot strip mills are precisely defined by various variables, which are taken directly froth the rolling schedule (separation force, torque. speed. strip thickness) or calculated from figures of the rolling schedule and dimensions of the mill (strip reduction, roll diameter etc.). These variables allow to describe the mechanical rolling conditions of all passe...

Abstract-A second-order dual to a nonlinear programming problem is formulated. This dual uses the Ritz John necessary optimality conditions instead of the Karush-Kuhn-Tucker necessary optimal&y conditions, and thus, does not require a constraint qualification. Weak, strong, strictconverse, and converse duality theorems between primal and dual problems are established. @ 2001 Elsevier Science Lt...

Abstract In this article, we extensively develop Carleman estimates for the wave equation and give some applications. We focus on the case of an observation of the flux on a part of the boundary satisfying the Gamma conditions of Lions. We will then consider two applications. The first one deals with the exact controllability problem for the wave equation with potential. Following the duality m...