Lectures notes

1. Introduction

2. Convex sets

3. Convex functions

4. Convex optimization problems

5. Duality

6. Approximation and fitting

7. Statistical estimation

8. Geometric problems

9. Numerical linear algebra background

10. Unconstrained minimization

11. Equality constrained minimization

12. Interior-point methods

13. Conclusions

Homework

Homework solutions and grades are posted on the EEweb course website. (Follow the links to “Assignments” or “Grades”.)

• Homework 1 (due 1/15). Exercises 2.5, 2.7, 2.12 (g) in the textbook, plus some additional problems. The last problem requires the Matlab file illumdata.m and the CVX software package.

• Homework 2 (due 1/22). Exercises 3.1, 3.19 (a), 3.21(a), 3.22 (c), 3.23(a), and some additional problems. The last problem requires the Matlab files spline_data.m and bsplines.m.

• Homework 3 (due 1/29). Exercises 3.42, 3.55, 4.8 (d,e), 4.13, and two additional problems. Note that older versions of the textbook had a typo in exercise 3.55: the last inequality should be h’(x) < 0.

• Homework 4 (due 2/5). Exercises 4.19, 4.26(a), 4.27, 4.29, and two additional problems.

• Homework 5 (due 2/12). Problem 3 requires the Matlab file log_opt_invest.m.

• Homework 6 (due 2/19). Exercises 5.12, 5.19, 5.29, and three additional problems.

• Homework 7 (due 2/26). Exercises 5.26, 5.33, and three additional problems.

• Homework 8 (due 3/5). The problems require the Matlab files pwl_gp_data.m and one_bit_measurements.m.

• Homework 9 (due 3/12).

Course information

Lectures: Dodd Hall 78. Tuesday & Thursday 10:00-11:50AM.

Textbook and lecture notes. The lecture notes are posted on this website. The textbook is Convex Optimization, available online and in hard copy at the UCLA bookstore. Some books that can serve as secondary (and entirely optional) reference texts are:

• A. Ben-Tal and A. Nemirovski, Lectures on Modern Convex Optimization, Society for Industrial and Applied Mathematics.

• D. Bertsekas, A. Nedic, A.E. Ozdaglar, Convex Analysis and Optimization, Athena Scientific.

• Y. Nesterov, Introductory Lectures on Convex Optimization: A Basic Course, Kluwer.

• J. M. Borwein and A. S. Lewis, Convex Analysis and Nonlinear Optimization, Springer.

• D. Bertsekas, Nonlinear Programming, Athena Scientific.

• D. Luenberger, Linear and Nonlinear Programming, Addison-Wesley.

• J. Nocedal and S. Wright, Numerical Optimization, Springer.

Course requirements. Weekly homework assignments; open-book final exam on Friday, March 20, 11:30-2:30PM.

Grading. Approximate weights in the final grade are: homework 25%, final exam 75%.

Software. We will use CVX, a Matlab software package for convex optimization.