Wireless Networking

APPENDIX C

Convex Optimization

We follow the notation and approach of the text by Bazaraa et al. [6].

C.1 Convexity

Definition C.1

A set χ ⊂ ⁿ is said to be convex if for any X₁, X₁ ε χ it holds that λx₁ + (1 − λ)x₂ ε χ, for every λ ε [0, 1].

Thus a set of real vectors is convex if the entire line segment joining any pair of elements of the set lies entirely within the set.

Definition C.2

χ is a convex set in ⁿ. A function f : χ → is said to ...