A Lagrange Multiplier Method for Semilinear Elliptic State Constrained\n Optimal Control Problems

2018/06/21 by Veronika Karl, Karl, Veronika, Ira Neitzel +3
Engineering · Computer Science · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Optimization and Variational Analysis #Differential Equations and Numerical Methods

paper · pdf · doi:10.48550/arxiv.1806.08124

Abstract

In this paper we apply an augmented Lagrange method to a class of semilinear\nelliptic optimal control problems with pointwise state constraints. We show\nstrong convergence of subsequences of the primal variables to a local solution\nof the original problem as well as weak convergence of the adjoint states and\nweak* convergence of the multipliers associated to the state constraint.\nMoreover, we show existence of stationary points in arbitrary small\nneighborhoods of local solutions of the original problem. Additionally, various\nnumerical results are presented.\n

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