Syllabus & Lectures

Syllabus

The most recent version of the syllabus can be found here (updated Nov 21, 2016).

Lectures

• Summer reading: Chapter 1 (Introduction), Boyd and Vandenberghe.
• Aug 25, 2016: Linear Algebra review
  Chapter 2.1, Boyd and Vandenberghe. Video of lecture here (note: there is audio disturbance in the recording until 5 mins in, at which point it was rectified). Lecture notes here.
• Aug 30, 2016: Affine sets, relative interior
  Chapter 2.1, 2.2, Boyd and Vandenberghe. Video of lecture here (note: audio disturbance again, fixed for future lectures. Also voice and video of out sync this time, put in a request to have it fixed.). Lecture notes here.
• Sep 1, 2016: Convex sets, cones, hyperplanes
  Chapter 2.2, Boyd and Vandenberghe. Video of lecture here. Lecture notes here.
• Sep 6, 2016: Polyhedra, operations preserving convexity of sets, generalized inequalities
  Chapter 2.2, 2.3, Boyd and Vandenberghe. Video of lecture here. Lecture notes here.
• Sep 8, 2016: Separating hyperplane theorem
  Chapter 2.4, 2.5, 2.6, Boyd and Vandenberghe. Video of lecture here. Lecture notes here.
• Sep 13, 2016: Dual cones
  Chapter 2.5, 2.6, Boyd and Vandenberghe. Video of lecture here. Lecture notes here.
• Sep 15, 2016: Convex functions, first-order conditions
  Chapter 3.1.1-3.1.3, Boyd and Vandenberghe. Video of lecture here. Lecture notes here.
• Sep 20, 2016: Second-order conditions, Jensen's inequality
  Chapter 3.1, Boyd and Vandenberghe. Video of lecture here. Lecture notes here.
• Sep 22, 2016: Operations which preserve convexity of functions
  Chapter 3.2, Boyd and Vandenberghe. Video of lecture here. Lecture notes here.
• Sep 27, 2016: Optimization problems
  Chapter 4.1, Boyd and Vandenberghe. Video of lecture here. Lecture notes here.
• Sep 29, 2016: Convex optimization problems
  Chapter 4.2, Boyd and Vandenberghe. Video of lecture here. Lecture notes here.
• Oct 4, 2016: Linear and quadratic programs
  Chapter 4.2-4.3 , Boyd and Vandenberghe. Video of lecture here. Lecture notes here.
• Oct 6, 2016: Second-order cone programs, geometric programs, semidefinite programs
  Chapter 4.3-4.4, Boyd and Vandenberghe. Video of lecture here. Lecture notes here.
• Oct 11, 2016: Semidefinite programs
  Chapter 4.62, Boyd and Vandenberghe. Video of lecture here. Lecture notes here.
• Oct 13, 2016: Lagrange dual problem
  Chapter 5.1, 5.2, Boyd and Vandenberghe. Video of lecture here. Lecture notes here.
• Oct 18, 2016: Strong duality, Minimax theorem, optimality conditions
  Chapter 5.2, 5.5, Boyd and Vandenberghe. Video of lecture here. Lecture notes here.
• Oct 20, 2016: No class (Reading Days)
• Oct 25, 2016: Integer programs, introduction to approximation algorithms, start primal-dual schema for Set Cover.
  Chapters 12 and 15, Vazirani (Approximation Algorithms). There is unfortunately no video of this lecture. Lecture notes here.
• Oct 27, 2016: Primal-dual schema: An approximation algorithm for Set Cover. Start LP Rounding: A 3/4 approximation algorithm for MAX-SAT.
  Chapters 15 and 16, Vazirani (Approximation Algorithms). Video of lecture here. Lecture notes here.
• November 1, 2016: Finish LP rounding for MAX-SAT. Start SDP Rounding: A 0.878-approximation algorithm for MAX-CUT.
  Chapter 26, Vazirani (Approximation Algorithms). Video of lecture here. Lecture notes here.
• November 3, 2016: No class
• November 8, 2016: Finish SDP Rounding: A 0.878-approximation algorithm for MAX-CUT.
  Chapter 26, Vazirani (Approximation Algorithms). Video of lecture here. Lecture notes here.
• November 10, 2016: Sum of squares proofs and SDPs.
  Barak and Steurer (Sum-of-Squares Proofs and the Quest toward Optimal Algorithms). Video of lecture here. Lecture notes here.
• November 15, 2016: Sum of squares proofs and SDPs, continued.
  Barak and Steurer (Sum-of-Squares Proofs and the Quest toward Optimal Algorithms). Video of lecture here. Lecture notes here.
• November 17, 2016: Gradient descent.
  Chapter 9.1-9.3, Boyd and Vandenberghe. Video of lecture here. Lecture notes here.
• November 22, 2016: Newton's method.
  Chapter 9.5, Boyd and Vandenberghe. Video of lecture here. Lecture notes here.
• November 23, 2016: No class (Thanksgiving)
• November 29, 2016: Newton's method with equality constraints.
  Chapter 10.1,10.2, Boyd and Vandenberghe. Video of lecture here. Lecture notes here.
• December 1, 2016: Interior point methods: Barrier method.
  Chapter 11.1-11.3, Boyd and Vandenberghe. Video of lecture here. Lecture notes here.