Second order necessary conditions of optimality for stochastic systems with variable delay

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...

A numerical approach for variable-order fractional unified chaotic systems with time-delay

This paper proposes a new computational scheme for approximating variable-order fractional integral operators by means of finite element scheme. This strategy is extended to approximate the solution of a class of variable-order fractional nonlinear systems with time-delay. Numerical simulations are analyzed in the perspective of the mean absolute error and experimental convergence order. To ill...

Second-order necessary optimality conditions for a discrete optimal control problem with mixed constraints

In this paper, we study second-order necessary optimality conditions for a discrete optimal control problem with nonconvex cost functions and state-control constraints. By establishing an abstract result on second-order necessary optimality conditions for a mathematical programming problem, we derive second-order necessary optimality conditions for a discrete optimal control problem.

Pointwise Second-Order Necessary Optimality Conditions for the Mayer Problem with Control Constraints

This paper is devoted to second order necessary optimality conditions for the Mayer optimal control problem when the control set U is a closed subset of R. We show that, in the absence of endpoint constraints, if an optimal control ū(·) is singular and integrable, then for almost every t such that ū(t) is in the interior of U , both the Goh and a generalized LegendreClebsch conditions hold true...