Optimization

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2

1-D Optimization Algorithms

2.1 Introduction

The one-dimensional (1-D) optimization problem refers to an objective func-

tion with one variable. In practice, optimization problems with many vari-

ables are complex, and rarely does one nd a problem with a single variable.

However, 1-D optimization algorithms form the basic building blocks for

multivariable algorithms. As these algorithms form a subproblem of mul-

tivariable optimization problems, numerous methods (or algorithms) have

been reported in the literature, each with some unique advantage over the

others. These algorithms are classied into gradient-based and non–gradient-

based a ...