First and second order necessary optimality conditions for stochastic distributed systems

Marginal values and second-order necessary conditions for optimality

Second Order Necessary and Sufficient Optimality Conditions under Abstract Constraints

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...

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...

First- and Second-Order Necessary Conditions Via Exact Penalty Functions

In this paper we study firstand second-order necessary conditions for nonlinear programming problems from the viewpoint of exact penalty functions. By applying the variational description of regular subgradients, we first establish necessary and sufficient conditions for a penalty term to be of KKT-type by using the regular subdifferential of the penalty term. In terms of the kernel of the subd...

Bianchini HIGH ORDER NECESSARY OPTIMALITY CONDITIONS

In this paper we present a method for determining some variations of a singular trajectory of an affine control system. These variations provide necessary optimality conditions which may distinguish between maximizing and minimizing problems. The generalized Legendre-Clebsch conditions are an example of these type of conditions.