Proximal Methods for Elliptic Optimal Control Problems with Sparsity Cost Functional

Directional Sparsity in Optimal Control of Partial Differential Equations

We study optimal control problems in which controls with certain sparsity patterns are preferred. For time-dependent problems the approach can be used to find locations for control devices that allow controlling the system in an optimal way over the entire time interval. The approach uses a nondifferentiable cost functional to implement the sparsity requirements; additionally, bound constraints...

Shape-Measure Method for Solving Elliptic Optimal Shape Problems (Fixed Control Case)

On goal-oriented adaptivity for elliptic optimal control problems

The paper proposes goal-oriented error estimation and mesh refinement for optimal control problems with elliptic PDE constraints using the value of the reduced cost functional as quantity of interest. Error representation, hierarchical error estimators, and greedy-style error indicators are derived and compared to their counterparts when using the all-at-once cost functional as quantity of inte...

Domain Identification Problem for Elliptic Hemivariational Inequalities

The domain identification problems for the elliptic hemivariational inequalities are studied. These problems are formulated as the optimal control problems with admissible domains as controls. The existence of optimal shapes is obtained by the direct method of calculus of variations for a l.s.c. cost functional.

Second-Order and Stability Analysis for State-Constrained Elliptic Optimal Control Problems with Sparse Controls

An optimal control problem for a semilinear elliptic partial differential equation is discussed subject to pointwise control constraints on the control and the state. The main novelty of the paper is the presence of the L1-norm of the control as part of the objective functional that eventually leads to sparsity of the optimal control functions. Second-order sufficient optimality conditions are ...