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 f_{0}(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 ∈ R^{n} the optimization variable and the function f_{0} : R^{n} → R the objective function or cost function. The inequalities f_{i}(x) ≤ 0 are called inequality constraints, and the corresponding functions f_{i} : R^{n} → R are called the inequality constraint functions. The equations h_{i}(x) = 0 are called the equality constraints, and the functions h_{i} : R^{n} → R are the

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