Optimal solution techniques for control problem of evolution equations

Abstract

A lot of optimal solution techniques exist in literature and have been employed to solve optimization problems. However, in this work, two optimal solution techniques namely the Steepest Descent Method (SDM) and the Extended Conjugate Gradient Method (ECGM) were  applied to two evolution equations to determine which best approximates the system to its analytic solution. Comparisons were  also carried out between the SDM and the ECGM for optimal solution and convergence. In doing so, the Liberty Basic Programming  Language (LBPL) was employed to perform various numerical iterations on the respective algorithms of the techniques. It was discovered  that the SDM proved to be a better technique in obtaining an optimal solution than the ECGM.