Optimality Conditions and Error Analysis of Semilinear Elliptic Control Problems with $L^1$ Cost Functional

Abstract

Abstract. Semilinear elliptic optimal control problems involving the L 1 norm of the control in the objective are considered. Necessary and sufficient second-order optimality conditions are derived. A priori finite element error estimates for piecewise constant discretizations for the control and piecewise linear discretizations of the state are shown. Error estimates for the variational discretization of the problem in the sense of [13] are also obtained. Numerical experiments confirm the convergence rates.Key words. optimal control of partial differential equations, non-differentiable objective, sparse controls, finite element discretization, a priori error estimates

Analytical, Optimal, and Sparse Optimal Control of Traveling Wave Solutions to Reaction-Diffusion Systems

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