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.

Learning outcomes

  • 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.

Further reading

  • Chapter 5.5 and 11.1-2 of Boyd and Vandenberghe.


  1. Stephen Boyd and Lieven Vandenberghe. Convex Optimization. Cambridge University Press, 2004.
  2. Jorge Nocedal and Stephen J.Wright. Numerical Optimization. Springer, 2006.
  3. Yuri Nesterov. Introductory Lectures on Convex Optimization. A basic course. Springer, 2004.
  4. Aaron Ben-Tal and Akadi Nemirovski. Lectures on Modern Convex Optimization. 2013.