Schedule - Spring 2018
Week 1
Mon 01/22 | Introduction: Basic terminology, examples: linear regression, LASSO, sparse regression | [pdf] [HTML] [IJulia] [data] |
Wed 01/24 | Elements of convex geometry: Convex sets, convex functions, separating hyperplanes, linear classification, perceptron, neural networks | [pdf (S16)] |
Fri 01/26 | Section 1 | [pdf (S16)] |
Week 2
Mon 01/29 | Linear programming: Definition, canonical and standard form, modelization examples | [pdf (S16)] [HTML] [IJulia] [data] |
Wed 01/31 | Duality in linear programming: Dual programs, weak duality, strong duality, complementary slackness, Farkas lemma. We largely followed lecture notes by S. Sachdeva. | |
Fri 02/02 | Section 2 | [pdf (S16)] |
Week 3
Mon 02/05 | Applications of duality: Game theory, Nash equilibrium, minimax theorem | [pdf (S16)] |
Wed 02/07 | Simplex algorithm: The simplex algoritm, extreme points. We mostly followed lecture notes by J. Nelson. | |
Fri 02/09 | Section 3 | [pdf (S16)] |
Week 4
Mon 02/12 | Simplex continued: Simplex algorithm review, why is the point maintained by the simplex a vertex? (e.g. see Theorem 3.2 in Bertsimas and Tsitsiklis). | |
Characterizations of convex functions: first order Taylor expansions, linear lower bounds to convex functions. | [pdf (S16)] | |
Wed 02/14 | Characterizations of convex functions (continued): global and local minima, second order Taylor expansions, Hessian characterization of convex functions. | [pdf (S16)] |