Optimal control theory of distributed parameter systems has been a very active field in recent years; however, very few books have been devoted to the study of computational algorithms for solving optimal control problems. For this reason we decided to write this book. Because the area is so broad, we confined ourselves to optimal control problems involving first and second boundary-value problems of a linear second-order parabolic partial differential equation. However, the technique's used are by no means restricted to these problems. They can be and in some cases already have been applied to problems involving other types of distributed parameter systems. Our aim is to devise computational algorithms for solving optimal control problems with particular emphasis on the mathematical theory underlying the algorithms. These algorithms are obtained by using a first-order strong variational method or gradient-type methods.
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