First and second order necessary conditions for stochastic optimal controls

Second-order Necessary Conditions for Optimal Impulsive Control

Second-order conditions of optimality for an impulsive control problem are presented and derived from those for an appropriate abstract optimization problem with equality, inequality and set inclusion constraints. An important feature of these conditions is that they do not degenerate for abnormal control processes in spite of the absence of a priori normality assumptions on the data of the pro...

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...

On necessary and sufficient conditions for near-optimal singular stochastic controls

This paper is concerned with necessary and sufficient conditions for near-optimal singular stochastic controls for systems driven by a nonlinear stochastic differential equations (SDEs in short). The proof of our result is based on Ekeland’s variational principle and some dilecate estimates of the state and adjoint processes. This result is a generalization of Zhou’s stochastic maximum principl...

Marginal values and second-order necessary conditions for optimality

First- and Second-order Necessary Conditions for Control Problems with Constraints

Second-order necessary conditions are developed for an abstract nonsmooth control problem with mixed state-control equality and inequality constraints as well as a constraint of the form G(x, u) e T, where T is a closed convex set of a Banach space with nonempty interior. The inequality constraints g{s, x, u) < 0 depend on a parameter 5 belonging to a compact metric space S. The equality constr...