Problems of economic system optimization with quadratic criteria and monotone controls. Some algorithms for their numerical solution

In this paper some numerical algorithms are presented to solve the Hamilton-Jacobi-Bellman equation associated to the optimal cost function corresponding to control problems of economic systems which involve the exploitation of non-renewable resources, i.e., the controls used are monotone (non-increasing or non-decreasing), and they may also be discontinuous. An almost complete study of this problem and of the theoretical characterization of its solution has been done. In that paper the solution of the problems is reduced to the treatment of the elliptic quasi-variational inequality in the interval [0,T]. In this paper an extension of the methodology to the analysis and numerical solution of this inequality is done. It gives three numerical algorithms, convergence properties of the discretization procedure is proven and comparative computational results are shown.