# EE236B - Convex Optimization (Winter Quarter 2014-15)

## Lecture notes

Introduction

Convex sets

Convex functions

Convex optimization problems

Duality

Approximation and fitting

Statistical estimation

Geometric problems

Numerical linear algebra background

Unconstrained minimization

Equality constrained minimization

Interior-point methods

Conclusions

## Homework

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

Homework 1 (due 1/15). The problem requires
the MATLAB file `illumdata.m`.

Homework 2 (due 1/22). Exercises T2.12 (d,e,g), T2.37 (b,c),
A5.8, and two additional problems.
Problem A5.8 requires the files `spline_data.m`
and `bsplines.m`.

Homework 3 (due 1/29). Exercises T3.19(a), A2.3, A2.10, A2.20,
A2.26, A5.4.
(Note that the 3rd sentence in problem A2.26 is incomplete:
‘where ’ should be: ‘where is the identity matrix’.)

Homework 4 (due 2/5). Exercises T3.55, A2.17, A2.21, A3.17, A7.9.

Homework 5 (due 2/12). Exercises A3.21, A5.9, T4.27, A12.6, and
an additional problem.

Homework 6 (due 2/19). Exercises A3.5, A3.11 (a,b,c), A3.13, A7.2,
A4.3, T5.21 (a,b,c).

Homework 7 (due 2/26).
Exercises T5.29, A4.4, A4.14, A4.17, A4.22, T5.30.

Homework 8 (due 3/5). Exercises A4.10, A4.18, A4.20, A6.5, A7.1, A7.7.
Problem A6.5 requires the file
`nonlin_meas_data.m`.

Homework is due at 4PM on the due date. It can be submitted in the
236B homework box in the TA meeting room (67-112 Engineering 4).

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 10:00-11:50AM.

**Textbook**
The textbook is *Convex
Optimization*, available online and in hard copy at the UCLA bookstore.
The following books are useful as 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 Monday, March 16, 8:00-11:00 AM.
The weights in the final grade are: homework 20%, final exam 80%.

**Software**.
We will use CVX,
a MATLAB software package for convex optimization.
Python users are welcome to use CVXPY instead of MATLAB
and CVX.