Electrical Engineering 364m: The Mathematics of Convexity

John Duchi, Stanford University, Winter 2024

Approximate course schedule

The syllabus below suggests what will (likely) be our approximate course schedule. The course will approximately track the schedule in EE364a, so that we can provide mathematical depth alongside the simultaneous material from EE364a. We will likely change a few things around as the course continues, and we may even omit topics or add others as the class desires.

Lecture	Date	Topics	Reading
1	Wed, Jan 10	Convex sets	HUL A
2	Wed, Jan 17	Convex functions	HUL B.1, B.2.5, D.1, E.1.1
3	Wed, Jan 24	Optimization problems (relaxations)	GW
4	Wed, Jan 31	Duality	Luenberger 8
5	Wed, Feb 7	Geometric problems	Ball Lecture 5
6	Wed, Feb 14	Cutting planes and center of gravity	BV, Grunbaum
7	Wed, Feb 21	Approximation and robustness	Polik and Terlaky
8	Wed, Feb 28	Self-concordant functions	Renegar, esp. Ch. 2.2–2.3
9	Wed, Mar 6	Self-concordant functions	Renegar, BE
10	Wed, Mar 13	Minimization algorithms	D & L

Abbreviation / Reference Key

HUL J.B. Hiriart-Urruty and C. Lemarechal, Fundamentals of Convex Analysis
Ball K. Ball, An Elementary Introduction to Modern Convex Geometry
D. Luenberger Optimization by Vector Space Methods
GW Goemans and Williamson, Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming
BV Bertsimas and Vempala, Solving convex programs by random walks
B. Grunbaum, Partitions of mass-distributions and of convex bodies by hyperplanes
I. Polik and T. Terlaky, A Survey of the S-Lemma
J. Renegar, A Mathematical View of Interior-Point Methods in Convex Optimization
BE S. Bubeck and R. Eldan, The entropic barrier: a simple and optimal universal self-concordant barrier
D & L D. Drusvyatskiy and A. Lewis, Error Bounds, Quadratic Growth, and Linear Convergence of Proximal Methods