Algorithms for Unconstrained Nonlinear Programming

Abstract

A library of algorithms, for solving unconstrained nonlinear programming problems

$$\mathop {\min }\limits_{x \in {R^n}} f\left( x \right),$$

(3.1)

has been presented in the mathematical programming literatures. There are many excellent books dealing with the algorithms comprehensively (to mention a few, Avriel [17], Bazaraa and Shetty [27], Fletcher [105], Gill, Murray and Wright [123], and Luenberger [205]). In this section we only introduce some basic algorithms which have already been frequently used or would be used in the future in artificial neural network study. The same consideration will be taken when we arrange the materials for the other chapters.