Numerical Methods and Optimization

Chapter 13

Unconstrained Optimization

In this chapter we deal with unconstrained optimization problems in the form

minimize f(x),

where f :IR

n

→ IR is a continuously differentiable function. We first develop

optimality conditions, which characterize analytical properties of local optima

and are fundamental for developing solution methods. Since computing not

only global but even local optimal solutions is a very challenging task in gen-

eral, we set a more realistic goal of finding a point that satisfies the first-order

necessary conditions, which are the conditions that the first-order derivative

(gradient) of the objective function must satisfy at a point ...