In Week 9 we will begin our study of non-linear convex optimization. Before deriving optimality conditions we begin with a discussion of an application of quadratic programming. Unconstrained quadratic optimization has featured before when discussing linear regression and least squares problem. We now learn how to deal with such problems in the presence of equality and inequality constraints.

Intended learning outcomes

  • Describe portfolio optimization as an application of quadratic programming
  • Derive Lagrange multipliers and Lagrangian duality.

Tasks and Materials

  • The lecture notes and the problem sheet are available in the Lectures and Assignemnts section, respectively.

Further reading

  • Lecture 14: Chapter 5.1-2 of Boyd and Vandenberghe.
  • An overview paper on practical issues related to portfolio optimization can be found here.


  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.