Abstract
The purpose of this paper is to establish a new approximation method using the penalty function for solving constrained optimal control problems defined in Banach spaces.
The principal advantages of the present method are as follows: (a) Both upper and lower bounds of the cost functional are obtained, (b) The functional which is introduced to obtain the approximate solution does not contain parameters approaching zero or infinity and (c) An approximate solution which satisfies all the constraints is obtained.
In this paper, the constraints are given by equalities and inequalities, and all these constraints are manipulated by embedding them in the penalty function.
