BASICS OF SET-CONSTRAINED AND UNCONSTRAINED OPTIMIZATION
In this chapter we consider the optimization problem
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 ...