Chapter 3: Optimization Theory for Communications

Learning Objectives

• Identify convex sets and convex functions, and verify convexity using definitions, gradient, and Hessian tests
• Formulate wireless resource-allocation problems as LPs, QPs, SOCPs, or SDPs and recognize their structure
• Derive and apply KKT conditions; solve water-filling problems algebraically and geometrically
• Implement gradient descent, projected gradient descent, and proximal methods; analyse convergence rates
• Understand Lagrangian duality, strong duality via Slater's condition, and dual decomposition for distributed optimization
• Recognise NP-hard combinatorial problems in wireless (scheduling, user selection) and apply LP/SDP relaxations