Electrical Engineering 364m: The Mathematics of Convexity
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
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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
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