CME307/MS&E311
Optimization
Winter 20162017

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Course Outline

Handouts

Assignments

Course Outline
Part I: Math Reviews and Math. Prog. Models
Math. Prog. Introduction
(Lecture Slide Note 1, L&Y Chapt 1)
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, ArrowDebreu's equilibrium, combinatorial auctions, sensor network localization, 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 secondorder 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 and nonconvex optimization
(Lecture Slide Notes 8 and 9, L&Y various chapters and new materials)
Part III: Math. Prog. Algorithms
Unconstrained optimization:
Basic descent methods, accelerated descent
(Lecture Slide Note 10, L&Y Chapter 8)
Newton's method, trust region problem
(Lecture Slide Note 11, L&Y Chapter 8)
Block coordinate method (with randomization), stochastic gradient
(Lecture Slide Note 12, L&Y Chapter 8)
Conjugate gradient method and Quasi Newton's method
(Lecture Slide Note 13, L&Y Chapters 9 and 10)
Linearly constrained optimization:
Interiorpoint algorithms for LP, SDP, and convex optimization
(Lecture Slide Note 14, L&Y Chapters 5 and 6)
Interiorpoint algorithms for nonconvex quadratic optimization
(Lecture Slide Note 15, new materials)
Firstorder interiorpoint methods
(Lecture Slide Note 16, L&Y Chapter 13 and new materials)
Alternating Direction with Multipliers and ADMM method (with randomization)
(Lecture Slide Note 17, L&Y Chapter 14 and new materials)
Nonlinearly constrained optimization:
Barrier and Penality methods
(Lecture Slide Note 18, Chapter 13)
Lagrangian relaxation method
(Lecture Slide Note 19, Chapter 14)
Sequential linearly constrained quadratic programing (LCQP) method
(Lecture Slide Note 20, new materials)
Sequential quadraticaaly constrained quadratic programing (QCQP) method
(Lecture Slide Note 20, new materils)
Other diverse families of methods (time permitting)