Lecture 16

Learning objectives

After this class, you should be able to:

1. Define quadratic programs, strict quadratic programs, vector progams, and positive semi-definite matrices.
2. Explain why it may not be feasible to relax quadratic progams in the manner used with integer linear programs.
3. Show how a strict quadratic programs can be relaxed to a vector program, and why an optimal solution to the vector progam gives a bound on the optimal solution to the strict quadratic program.
4. Formulate MAX-CUT as a strict quadratic program and relax it to a vector program.

Reading assignment

1. Sections 26.1 and 26.2.

Exercises and review questions

• Questions on current lecture's material
  1. Explain the proof of theorem 26.3.

• Questions on next lecture's material
  1. None.