Additional Exercises for Convex Optimization - Stanford University

This is a collection of additional exercises, meant to supplement those found in the bookConvex
Optimization, by Stephen Boyd and Lieven Vandenberghe. These exercises were used in several
courses on convex optimization, EE364a (Stanford), EE236b (UCLA), or 6.975 (MIT), usually for
homework, but sometimes as exam questions. Some of the exercises were originally written for the
book, but were removed at some point.
Many of them include a computational component using one of the software packages for convex
optimization: CVX (Matlab), CVXPY (Python), or Convex.jl (Julia). We refer to these collectively
as CVX*. (Some problems have not yet been updated for all three languages.) The les required
for these exercises can be found at the book web sitewww.stanford.edu/~boyd/cvxbook/.
You are free to use these exercises any way you like (for example in a course you teach), provided
you acknowledge the source. In turn, we gratefully acknowledge the teaching assistants (and in
some cases, students) who have helped us develop and debug these exercises. Pablo Parrilo helped
develop some of the exercises that were originally used in MIT 6.975, Sanjay Lall developed some
other problems when he taught EE364a, and the instructors of EE364a during summer quarters
developed others.
We'll update this document as new exercises become available, so the exercise numbers and
sections will occasionally change. We have categorized the exercises into sections that follow the
book chapters, as well as various additional application areas. Some exercises t into more than
one section, or don't t well into any section, so we have just arbitrarily assigned these.
Course instructors can obtain solutions to these exercises by email to us. Please specify the
course you are teaching and give its URL.
Stephen Boyd and Lieven Vandenberghe
1
Contents
1 Convex sets3
2 Convex functions
6
3 Convex optimization problems
20
4 Duality41
5 Approximation and tting
60
6 Statistical estimation
78
7 Geometry98
8 Unconstrained and equality constrained minimization
115
9 Interior point methods
122
10 Mathematical background
131
11 Circuit design
133
12 Signal processing and communications
141
13 Control and trajectory optimization
153
14 Finance162
15 Mechanical and aerospace engineering
186
16 Graphs and networks
197
17 Energy and power
205
18 Miscellaneous applications
219