CO463/663 Fall 2009

Convex Optimization and Analysis

    "The great watershed in optimization is not between linearity and nonlinearity, but convexity and nonconvexity." ( Rockafellar, 1993.)

Instructor Henry Wolkowicz (MC6065, x35589)

  • Time: 2:30-3:50PM, TTh
  • Location: MC4044
  • Office Hours: Thursday 4-5PM or
  • FINAL EXAM: Thurs. Dec. 10, RCH 206, 9-11:30AM.


  • Text:
  • Course Outline; (Chapters 1,2,3,4, and 6.1-3, 7.1-2.)
  • Lecture outlines
  • Further References (Supplementary Reference by Bertsekas is on 3 hour reserve; Call number: T57.815 .B47x 2009)
  • Marking Scheme: HW 50%; Final 50%; Final exam from Fall 2002
  • HOMEWORK (and solutions):
    Expect 4-6 assignments - to be submitted at the beginning of the class stated on the assignment.
    HW1; HW2; HW3; HW4;



    1. Homework #1
    2. Homework #2
      Due: Tuesday, Oct. 20, 2009
      Reading
      Problems/Tasks
      • CVX Problem:
        • consider the SDP relaxation of the max-cut problem discussed in class. Solve the dual of the relaxation using CVX. Let y,X denote the optimum of the dual and primal, respectively.
        • Generate random data as input, i.e. generate random nonnegative weights for the graph and input the Laplacian L as data for the SDP problem.
        • Find an (approximate) solution x for the original max-cut problem and calculate a percentage error.
        • Hand in your cvx program and: L; primal dual optimal y, X; the approximate x; and the percentage error.
        • Perform the above for dimension n=3,5,10
      • Assignment 2 problems pdf file;
    3. Homework #3
      Due: Thursday, Nov. 12, 2009
      Reading
      Problems/Tasks
    4. Homework #4
      Due: Thursday, Dec. 3, 2009
      Reading
      • Text: Related sections.
      Problems/Tasks


    CVX Tests/Files




  • Last Modified:  Monday 8 October 2012