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An Introduction to Optimization, 4th Edition by Stanislaw H. Zak, Edwin K. P. Chong

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CHAPTER 6

BASICS OF SET-CONSTRAINED AND UNCONSTRAINED OPTIMIZATION

6.1 Introduction

In this chapter we consider the optimization problem

equation

The function f : n that we wish to minimize is a real-valued function called the objective function or cost function. The vector x is an n-vector of independent variables: x = [x1, x2, …, xn] n. The variables x1, …, xn are often referred to as decision variables. The set Ω is a subset of n called the constraint set or feasible set.

The optimization problem above can be viewed as a decision problem that involves finding the “best” vector x of the decision variables over all possible vectors in Ω. By the “best” vector we mean the one that results in the-smallest value of the objective function. This vector is called the minimizer of f over Ω. It is possible ...

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