# EE236B - Convex Optimization (Winter Quarter 2015-16)

## 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 1/14). The problem requires
the MATLAB files `circlefit.m` and
`illumdata.m`.

Homework 2 (due **Tuesday 1/26**). Exercises T2.12 (d,e,g), A5.8, and
three additional problems.
Problem A5.8 requires the files `spline_data.m`
and `bsplines.m`.

Homework 3 (due Thursday 2/4). Exercises T3.2, T3.19 (a), T3.23 (a),
T3.55, A2.10, A2.20 (b), A2.21, A3.17
and two additional problems.

Homework 4 (due 2/11). Exercises A3.5, T4.13, T4.21 (b), A3.29,
T4.25, A3.21, A7.9.

Homework 5 (due 2/18). Exercises T4.43 (b, c), A3.11, A3.12,
T5.12, T5.21 (a,b,c), and an additional problem.

Homework is due at 4PM on the due date. It can be submitted at the
start of the lecture or in the EE236B 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**: Franz Hall 1260, Tuesday & Thursday 16:00-17:50PM.

**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 Tuesday, March 15, 3:00-6:00 PM.
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.