SECOND ORDER SUFFICIENT OPTIMALITY CONDITIONS FOR SEMILINEAR ELLIPTIC CONTROL PROBLEM OF INFINITE ORDER

Second Order Sufficient Optimality Conditions for Some State-constrained Control Problems of Semilinear Elliptic Equations

This paper deals with a class of optimal control problems governed by elliptic equations with nonlinear boundary condition. The case of boundary control is studied. Pointwise constraints on the control and certain equality and set{constraints on the state are considered. Second order suucient conditions for local optimality of controls are established.

Second-order Sufficient Optimality Conditions for a Semilinear Optimal Control Problem with Nonlocal Radiation Interface Conditions

We consider a control constrained optimal control problem governed by a semilinear elliptic equation with nonlocal interface conditions. These conditions occur during the modeling of diffusegray conductive-radiative heat transfer. After stating first-order necessary conditions, second-order sufficient conditions are derived that account for strongly active sets. These conditions ensure local op...

Verification of Second-Order Sufficient Optimality Conditions for Semilinear Elliptic and Parabolic Control Problems

Sufficient Second-Order Optimality Conditions for an Elliptic Optimal Control Problem with Pointwise Control-State Constraints

An optimal control problem for an semilinear elliptic equation is investigated, where pointwise constraints are given on the control and the state. The state constraints are of mixed (bottleneck) type, where associated Lagrange multipliers can assumed to be bounded and measurable functions. Based on this property, a second-order sufficient optimality condition is established that considers stro...

Sufficient Second-Order Optimality Conditions for Semilinear Control Problems with Pointwise State Constraints

Abstract. Second-order sufficient optimality conditions are established for the optimal control of semilinear elliptic and parabolic equations with pointwise constraints on the control and the state. In contrast to former publications on this subject, the cone of critical directions is the smallest possible in the sense that the second-order sufficient conditions are the closest to the associat...