Convex Optimization

Chapter 9

Unconstrained minimization

9.1 Unconstrained minimization problems

In this chapter we discuss methods for solving the unconstrained optimization problem

(9.1)

where f : Rⁿ → R is convex and twice continuously differentiable (which implies that dom f is open). We will assume that the problem is solvable, i.e., there exists an optimal point x. (More precisely, the assumptions later in the chapter will imply that x exists and is unique.) ...