Unconstrained optimization

Abstract

The previous chapter presented a small sample of nonlinear optimization problems that might occur in practice; some of these had constraints on their variables and others did not. From this chapter onwards we will discuss ways to solve various types of optimization problems stated in terms of minimization. This is not really restrictive for we have already shown in (8.3) how to convert maximization problems to minimization problems. Our discussion will emphasize algorithms to solve nonlinear minimization problems and develop ways to determine if, in practice, the algorithms described are behaving as expected. Moreover, our discussion will strive to provide an understanding of optimality criteria, how they motivate the development of algorithms, and how they are used in determining if an optimal solution has been found.