Convex Optimization

Chapter 4

Convex optimization problems

4.1 Optimization problems

4.1.1  Basic terminology

We use the notation

(4.1)

to describe the problem of finding an x that minimizes f₀(x) among all x that satisfy the conditions f_i(x) ≤ 0, i = 1, . . . , m, and h_i(x) = 0, i = 1, . . . , p. We call x ∈ Rⁿ the optimization variable and the function f₀ : Rⁿ → R the objective function or cost function. The inequalities f_i(x) ≤ 0 are called inequality constraints, and the corresponding functions f_i : Rⁿ → R are called the inequality constraint functions. The equations h_i(x) = 0 are called the equality constraints, and the functions h_i : Rⁿ → R are the