Abstract
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 sufficient conditions for local optimality of controls are established.
Highlights
In contrast to the optimal control of linear systems with a convex objective, where first order necessary optimality conditions are already sufficient for optimality, higher order conditions such as second order sufficient optimality conditions (SSC) should be employed to verify optimality for nonlinear systems
Second order sufficient optimality conditions have proved to be useful for showing important properties of optimal control problems such as local uniqueness of optimal controls and their stability with respect to certain perturbations
We refer to the general expositions by Maurer and Zowe [15] and Maurer [14] for different aspects of second order sufficient optimality conditions
Summary
In contrast to the optimal control of linear systems with a convex objective, where first order necessary optimality conditions are already sufficient for optimality, higher order conditions such as second order sufficient optimality conditions (SSC) should be employed to verify optimality for nonlinear systems. Boundary control, semilinear elliptic equations, sufficient optimality conditions, state constraints We aimed to establish second order sufficient optimality conditions for boundary control problems governed by semilinear elliptic equations in domains of arbitrary dimension with general pointwise constraints on the control and the state.
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