On The Algorithm for Dynamic Restoring Control Problems with Matrix Coefficients

Abstract

An algorithm is hereby developed to solve a class of control problems constrained by dynamic restoring type with matrix coefficients numerically. The penalty-multiplier method is evolved to obtain an unconstrained discretized formulation. With the bilinear form expression, an associated operator is constructed via a theorem to circumvent the cumbersomeness inherent in some earlier methods; particularly the Function space algorithm (FSA).The conjugate gradient method (CGM) is evoked to solve the discretized problem. One sampled problem is solved numerically and the convergence analysis is found to be linearly convergent as demonstrated in the output data tables.

Keywords: Penalty-Multiplier, matrix coefficients, operator and linear convergence.