ON SECOND ORDER NECESSARY OPTIMALITY CONDITIONS FOR VECTOR OPTIMIZATION PROBLEMS

Sufficient Second Order Optimality Conditions for C Multiobjective Optimization Problems

In this work, we use the notion of Approximate Hessian introduced by Jeyakumar and Luc [19], and a special scalarization to establish sufficient optimality conditions for constrained multiobjective optimization problems. Throughout this paper, the data are assumed to be of class C, but not necessarily of class C.

Second-Order Necessary and Sufficient Optimality Conditions for Optimization Problems and Applications to Control Theory

This paper deals with a class of nonlinear optimization problems in a function space, where the solution is restricted by pointwise upper and lower bounds and by finitely many equality and inequality constraints of functional type. Second-order necessary and sufficient optimality conditions are established, where the cone of critical directions is arbitrarily close to the form which is expected...

Second- and First-Order Optimality Conditions in Vector Optimization

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...

Marginal values and second-order necessary conditions for optimality

On second – order conditions in vector optimization

Starting from second-order conditions for C scalar unconstrained optimization problems described in terms of the second-order Dini directional derivative, we pose the problem, whether similar conditions for C vector optimization problems can be derived. We define second-order Dini directional derivatives for vector functions and apply them to formulate such conditions as a Conjecture. The proof...