ABSTRACT
This chapter considers several iterative techniques for solving an unconstrained optimization problem. These techniques usually require many iterations of rather tedious computations. The chapter presents a large number of these techniques, and introduces an iterative search techniques for unconstrained optimization problems. It also considers linear search techniques, that is, finding a maximum or a minimum of the objective function along a straight line. Many of the multidimensional search techniques require a sequence of unidimensional (line) searches. Another way of locating the minimum value of a unimodal function f of a single real variable is to "fit" a polynomial p to f and then locate the minimum of the polynomial. The chapter provides several of these techniques, each using a quadratic polynomial. The first two techniques, Powell's algorithm and the Davies, Swann and Campey algorithm (DSC), are both concerned with the fitting of a quadratic polynomial to three points.
