Optimal Control of Nonlinear Elliptic Problems with Sparsity

Proximal Methods for Elliptic Optimal Control Problems with Sparsity Cost Functional

First-order proximal methods that solve linear and bilinear elliptic optimal control problems with a sparsity cost functional are discussed. In particular, fast convergence of these methods is proved. For benchmarking purposes, inexact proximal schemes are compared to an inexact semismooth Newton method. Results of numerical experiments are presented to demonstrate the computational effectivene...

Annular and sectorial sparsity in optimal control of elliptic equations

In this paper we consider optimal control problems in which a certain L1-type norm of the control appears in the objective. Problems of this type are of interest for at least two reasons. Firstly, the L1 norm of the control is often a natural measure of the control cost. Secondly, this term promotes sparsely supported optimal controls, i.e., controls which are zero on substantial parts of its d...

Optimal Control of Semilinear Elliptic Obstacle Problems

Integrating Differential Evolution Algorithm with Modified Hybrid GA for Solving Nonlinear Optimal Control Problems

‎Here‎, ‎we give a two phases algorithm based on integrating differential evolution (DE) algorithm with modified hybrid genetic algorithm (MHGA) for solving the associated nonlinear programming problem of a nonlinear optimal control problem‎. ‎In the first phase‎, ‎DE starts with a completely random initial population where each individual‎, ‎or solution‎...

Discretization-Optimization Methods for Nonlinear Elliptic Relaxed Optimal Control Problems with State Constraints

We consider an optimal control problem described by a second order elliptic boundary value problem, jointly nonlinear in the state and control with high monotone nonlinearity in the state, with control and state constraints, where the state constraints and cost functional involve also the state gradient. Since no convexity assumptions are made, the problem may have no classical solutions, and s...