CS 730: Nonlinear Optimization II - Spring 2019


Lecture: 11:00-12:15 MWF, Computer Sciences 1221
Class Mailing List: compsci730-1-s19@lists.wisc.edu
Mail Instructor: swright AT cs.wisc.edu
Course URL: http://www.cs.wisc.edu/~swright/cs730-s19.html
Canvas: https://canvas.wisc.edu/courses/127579

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 2-3

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

Course notes from 2015 are posted here. They are mostly for my own benefit and hence are terse, and refer heavily to the text in places. The topics will be somewhat different this semester, but similar enough to these notes to give you some idea what to expect.


Course Outline (subject to revision)

  • 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 Canvas

  • 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 Monday 6 May 2019, 2:45pm-4:45pm.


Will be posted on Canvas.

Handouts and Examples