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

Exercise numbers with prefix ’T’ refer to the textbook. Exercise numbers with prefix ’A’ refer to the collection of additional exercises on the textbook page.

• Homework 1 (due 4/11). The second problem requires the MATLAB file illumdata.m.

• Homework 2 (due 4/18). Exercises T2.12 (d,e,g), A7.2 (a,b), A2.25, A2.10, A2.20 (a), A5.8. Problem A5.8 requires the files spline_data.m and bsplines.m.

• Homework 3 (due 4/25). Exercises A2.3, A2.5, A2.17, A2.20 (b,c), A2.21, A3.27. Problem A3.27 requires the file affine_pol_data.m.

• Homework 4 (due 5/2). Exercises T4.29, A3.21, A3.11, A5.9, A7.9.

• Homework 5 (due 5/9). Exercises A3.13, T5.11, A4.3, T5.21 (a,b,c), A4.14 and an additional problem.

• Homework 6 (due 5/16). Exercises T5.26, A4.20, A4.10, A4.17, A12.12, A5.4.

• Homework 7 (due 5/23). Exercises A4.6, T5.29, A6.1, T7.4, A6.5, A7.1. Problem A6.5 requires the file nonlin_meas_data.m.

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

Course information

Lectures: Boelter 5440. Tuesday & Thursday 12:00-1:50PM.

Textbook The textbook is Convex Optimization, available online and in hard copy at the UCLA bookstore. The following books are useful as (optional) reference texts.

• A. Ben-Tal and A. Nemirovski, Lectures on Modern Convex Optimization (SIAM).

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

• D. Bertsekas, Convex Optimization Theory (Athena Scientific).

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

• J.B. Hiriart-Urruty and C. Lemarechal, Convex Analysis and Minimization Algorithms (Springer).

• D. Luenberger and Y. Ye, Linear and Nonlinear Programming (Springer).

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

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

Course requirements. Weekly homework assignments; open-book final exam on Wednesday, June 12, 11:30-2:30PM. The weights in the final grade are: homework 20%, final exam 80%.

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