In Week 10 we will derive the famous Karush-Kuhn-Tucker (KKT) conditions for constrained optimization problems. These conditions generalize the method of Lagrange multipliers and provide optimality conditions for non-linear constrained optimization problems. Based on these conditions, we will learn how to solve non-linear convex optimization problems.
- Understand Lagrangian duality and its special cases.
- Know the Karush-Kuhn-Tucker conditions and how to apply them.
- Understand the log-barrier and and its relation to interior point methods.
Tasks and Materials
- The lecture notes and problem sheets are available in their respective sections.
- Chapter 5.5 and 11.1-2 of Boyd and Vandenberghe.
- Stephen Boyd and Lieven Vandenberghe. Convex Optimization. Cambridge University Press, 2004.
- Jorge Nocedal and Stephen J.Wright. Numerical Optimization. Springer, 2006.
- Yuri Nesterov. Introductory Lectures on Convex Optimization. A basic course. Springer, 2004.
- Aaron Ben-Tal and Akadi Nemirovski. Lectures on Modern Convex Optimization. 2013.