Applied Mathematical Methods

24

Constrained Optimization

The area of constrained optimization is vast, with too many equally important competing methods. An exposition of those methods in detail is out of the scope of this book. But, even modest problems of optimization sometimes involve constraints that need to be handled for their solution. Therefore, in this chapter, we try to develop the fundamental ideas of constrained optimization, as a necessary analytical background.

Constraints

The typical form of the statement of a constrained optimization problem is the following.

Minimize   f (x)

subject to   g_i(x) ≤ 0   for i = 1, 2, …, l,   or g (x) ≤ 0;          (24.1)

          and   h_j (x) = 0   for j = 1, 2,…, m,   or h(x) = 0

Conceptually, it can be considered as “minimize ...