SURVEY ON SOLVING THE OPTIMAL CONTROL PROBLEM CONSTRAINTED BY LINEAR PARABOLIC EVOLUTION EQUATIONS BASED ON WAVELET FUNCTIONS

In this paper, an algorithm based on Petrov-Galerkin s method with wavelet basis functions are proposed for optimal con- trol problems governed by linear parabolic evolution equations. In these problems, the cost functional of control problem involves the terms of state and control variables that are expressed in terms of Sobolev norms. In this algorithm, we discretize the problem in time to obtain a linear system of equations in terms of state and control variables. In continuation, by finite differences, Riesz op- erator and the variation of the functional, we convert the above system only in terms of the control variables and solve the resulted system by numerical methods such as CG algorithm.