A global convergent semi-smooth Newton method for semi-linear elliptic optimal control problem. (15th August 2022) - Zhang, Zemian; Chen, Xuesong
Abstract: Global convergent semi-smooth Newton (GCSSN) method for L 2 -norm control constrained elliptic optimal control problem with L 1 -control cost is discussed. The first order necessary optimality conditions are analyzed and reduced system is proposed. After finite difference discretization, we propose the global convergent semi-smooth Newton method for discrete reduced system with the nonmonotone line search. The local superlinear convergence rate and convergence are proved theoretically. The demonstrated theoretical properties are verified with numerical results. To illustrate the effectiveness and efficiency, we compare the proposed method with semi-smooth Newton method in the simulation part. Graphical abstract: Highlights: Global convergent semi-smooth Newton method for semi-linear elliptic optimal control problem is proposed. We obtain the first order optimality necessary condition for optimal control problem. The convergence properties of algorithm are proven theoretically and verified by simulations.