Fundamentals of unconstrained optimization

Abstract

Non-linear optimization is concerned with methods for locating the least value (the minimum) or the greatest value (the maximum) of a non-linear function of any number of independent variables, referred to as the objective function. The least value problem is called minimization and the greatest value problem maximization. Any maximization problem can be converted into a minimization problem by multiplying the objective function by a factor of −1. It is therefore not necessary to consider these two aspects of the problem separately. In this book we adopt the more usual convention of discussing the entire subject in terms pertaining to minimization. When the problem is to be solved subject to no special conditions upon the values that the independent variables are allowed to assume, it is said to be unconstrained, otherwise it is constrained and these extra conditions are called constraints. Chapters 1 to 4 of this book deal with unconstrained optimization and chapters 5 to 7 with constrained optimization.