CS 730: Nonlinear Optimization II - Spring 2016


Lecture: 11:00-12:15 MWF, Computer Sciences 1257
Class Mailing List: compsci730-1-s16@lists.wisc.edu (here's the archive)
Mail Instructor: swright AT cs.wisc.edu
Course URL: http://www.cs.wisc.edu/~swright/cs730-s16.html
Piazza Home Page: https://piazza.com/wisc/spring2016/cs730

In general, classes will be held on MWF every week, and lectures will be 60 minutes, but may take up the full 75-minutes slot on several occasions. I will be absent on a number of MWF days, and the longer lectures will make up for these absences. Class time will average 150 minutes/week.

Instructor: Steve Wright

Office: 4379 CS
Office Hours: (tentatively) Monday 3-4, Thursday 3-4

General Course Information


  • CS / ISyE 726 or equivalent. (See me if you think you have done an equivalent course.)


  • J. Nocedal and S. J. Wright, Numerical Optimization, Second Edition, Springer, 2006. (It's essential to get the second edition! The version published in China in 2006 is a reprint of the first edition, so is not suitable.) Here is the current list of typos.


  • D. P. Bertsekas, with A. Nedic and A. Ozdaglar, Convex Analysis and Optimization, Athena Scientific, Belmont, MA, 2003.
  • S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press. Available here.
  • D. P. Bertsekas, Nonlinear Programming, Second Edition, Athena Scientific, Belmont, MA, 1999.
  • R. Fletcher, Practical Methods of Optimization, 2nd Edition, Wiley, Chichester & New York, 1987.
  • R. T. Rockafellar and R. J.-B. Wets, Variational Analysis, Springer, 1998. (This is a more advanced book and an invaluable reference.)
  • A. Ruszczynski, Nonlinear Optimization, Princeton University Press, 2006.
  • S. J. Wright, Primal-Dual Interior-Point Methods, SIAM, 1997. SIAM ebook is available here.

(All have been placed on reserve at the Wendt Library.)

Lecture Notes

These can be found here are updated sporadically. They are mostly for my own benefit and hence are terse, and refer heavily to the text in places. I supply them to help you fill in any missing details in the notes that you take in class.


Course Outline

  • Geometric viewpoint of constrained optimization
    • Convex sets, cones, projections
    • Tangent and normal to polyhedral sets
    • Theorems of the alternative, separation results
    • First-order conditions: polyhedral case
  • Stochastic Gradient
  • Optimality conditions for nonlinear programming
    • Constraint qualifications
    • First-order conditions and saddle points
    • Second-order conditions and critical cones
    • Degeneracy
  • Duality for nonlinear programming, including Wolfe and Fenchel duality
  • Nonlinear programming algorithms
    • Fundamentals: merit functions and filters, Maratos effect.
    • Interior-point and augmented Lagrangian methods
    • Sequential quadratic programming
  • Second-order cone programming and semidefinite programming: applications, barrier methods.


(The scheme below is provisional and subject to change until the third week of semester.)

First, some rules. I'm serious about these! Violations will be penalized energetically.

  • Submitting someone else's work as your own is academic misconduct. Such cheating and plagiarism will be dealt with in accordance with University procedures (see the Academic Misconduct page).
  • You may discuss homework with classmates. However, you may not share any code, carry out the assignment together, or copy solutions from another person. Discussion should be verbal only. The submitted version must be worked out, written, and submitted by you alone.
  • You may not discuss take-home exams with anyone while they are in progress, except the Instructor.

Keep track of your grades through the learn@uw system.

  • Approximately 8 homework assignments, 35% of grade. Some of these will be graded by class members, using a key supplied by me.
    • Homework is due at the beginning of class on the designated date.
    • No homework or project is accepted in mailbox of instructor.
  • MIDTERM, approx 25% of grade. (Probably a take-home.)
  • FINAL, approx 40% of grade. We will probably have a take-home exam that is due at the end of the scheduled exam time, and possibly will be submitted online. The nominal date/time for the final is Friday 13 May 2016, 2:45pm-4:45pm.


Previous Exams

Handouts and Examples