In this paper we discuss second order optimality conditions in optimization problems subject to abstract constraints. Our analysis is based on various concepts of second order tangent sets and parametric duality. We introduce a condition, called second order regularity, under which there is no gap between the corresponding second order necessary and second order suucient conditions. We show tha...

State Constrained Control-Affine Parabolic Problems II: Second Order Sufficient Optimality Conditions

In this paper we derive for a controlled stochastic evolution system on Hilbert space H a sufficient condition for optimality. The result is derived by using its adjoint backward stochastic evolution equation.

Introduction. Let M be an analytic n manifold and # = {X : a e A} a collection of analytic vector fields on M. A continuous map M, T > 0, is called a solution of,_!, tt)9 i = 1, —, k. We denote by s...

This paper is concerned with deriving necessary and sufficient optimality conditions for a fuzzy linear programming problem. Toward this end, an equivalence between fuzzy and crisp linear programming problems is established by means of a specific ranking function. Under this setting, a main theorem gives optimality conditions which do not seem to be in conflict with the so-called Karush-Kuhn-Tu...

In this paper sufficient second order optimality conditions for optimal control problems subject to stationary variational inequalities of obstacle type are derived. Since optimality conditions for such problems always involve measures as Lagrange multipliers, which impede the use of efficient Newton type methods, a family of regularized problems is introduced. Second order sufficient optimalit...

We establish new necessary and sufficient optimality conditions for optimization problems. In particular, we establish tractable optimality conditions for the problems of minimizing a weakly convex or concave function subject to standard constraints, such as box constraints, binary constraints, and simplex constraints. Our main theoretical tool for establishing these optimality conditions is ab...