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)]