Mathematical Preliminaries
(Lecture Slide Note 1, L&Y Appdendices A and C)
Math. Prog. Models and Applications: logistic regression, sparse regression, facility locations, support vector machines,
Fisher's pricing model, Arrow-Debreu's equilibrium,
combinatorial auctions, sensor network localization, MDP/Stochastic Game, etc.
(Lecture Slide Note 2, L&Y various chapters and new materials)
Part II: Math. Prog. Theories
Elements of Convex Analysis and Conic Duality
(Lecture Slide Note 3, L&Y Appendex B, Chapters 4 and 6)
Strong Conic Duality and Conic Linear Optimization
(Lecture Slide Note 4, L&Y Chapters 4 and 6)
First- and second-order optimality conditions
(Lecture Slide Notes 5 and 6, L&Y Chapters 7 and 11)
Lagrangian and duality theory
(Lecture Slide Note 7, L&Y Chapter 14)
Duality properties and applications for convex, nonconvex, and distributionally robust optimization
(Lecture Slide Notes 8 and 9, L&Y various chapters and new materials)