This page collects together the posts for the graduate course on optimization I taught at Princeton in the Spring 2013. This material has been reorganized (some parts have been cut, some have been extended) into a monograph when I taught the course for the second time in the Spring 2014.
Part I: Computational complexity of optimization
Post 1: Introduction
Post 2: The ellipsoid method
Post 3: LP, SDP, and Conic Programming
Post 4: Interior Point Methods
Post 5: IPMs for LPs and SDPs
Post 6: Lagrangian duality
Post 7: Classification, SVM, Kernel Learning
Post 8: Turing Machines
Post 9: P vs. NP, NP-completeness
Post 10: Getting around NP-hardness
Bonus lectures by Amir Ali Ahmadi: Sum of Squares (SOS) Techniques: An Introduction, Part I, and Part II
Part II: Oracle complexity of optimization
Post 11: Oracle complexity, large-scale optimization
Post 12: Oracle complexity of Lipschitz convex functions
Post 13: Oracle complexity of smooth convex functions
Post 14: Nesterov’s Accelerated Gradient Descent
Post 15: Strong convexity (added in 2014: Nesterov’s Accelerated Gradient Descent for Smooth and Strongly Convex Optimization)
Post 16: Conditional Gradient Descent and Structured Sparsity
Post 17: ISTA and FISTA
Post 18: Mirror Descent, part I/II
Post 19: Mirror Descent, part II/II
Post 20: Mirror Prox
Part III: Optimization and Randomness
Post 21: Noisy oracles (for stochastic approximation and acceleration by randomization)
Post 22: Acceleration by randomization for a sum of smooth and strongly convex functions
Post 23: Optimization with bandit feedback
Final exam
Post 24: An SDP based on Grothendieck’s inequality; Coordinate Descent
By Hog August 18, 2014 - 12:29 pm
Great blog!
By fetullah bayır February 16, 2014 - 3:57 am
Nice post. Many thanks for sharing!
By Evden eve nakliyat September 9, 2013 - 12:57 pm
Nice post. Many thanks for sharing!
By Nat Padmanabhan June 17, 2013 - 4:41 pm
Great blog! Thanks for pointing to the accelerated gradient method. Hope one day you record your lectures for the world to view and benefit from!
By Stephen Becker May 27, 2013 - 7:59 am
Well written and covers a timely choice of topics. Very nice! Thanks for taking the time to write this up.
By Matthieu Durut April 19, 2013 - 11:50 am
Very interesting blog, thanks for this