Convex and Nonsmooth Optimization

CSCI-GA.2945.002/ MATH-GA.2012.002 Selected Topics in Numerical Analysis

Mondays 5:10-7:00, Spring 2016, WWH 317

Instructor: Michael L. Overton

Course Description

Convex optimization problems have many important properties, including a powerful duality theory and the property that any local minimum is also a global minimum. Nonsmooth optimization refers to minimization of functions that are not necessarily convex, usually locally Lipschitz, and typically not differentiable at their minimizers. Topics in convex optimization that will be covered include duality, CVX ("disciplined convex programming"), gradient and Newton methods, Nesterov's optimal gradient method, the alternating direction method of multipliers, the primal barrier method, primal-dual interior-point methods for linear and semidefinite programs. Topics in nonsmooth optimization that will be covered include subgradients and subdifferentials, Clarke regularity, and algorithms, including gradient sampling and BFGS, for nonsmooth, nonconvex optimization. Homework will be assigned, both mathematical and computational. Students may submit a final project on a pre-approved topic or take a written final exam.

Prerequisites

Undergraduate linear algebra and multivariable calculus

Required Text Book for first part of course

Required Software Other Recommended Books and Resources: not required for course

Tentative Lecture Plan

Homework

Requirements
Attend class, submit all homeworks, and either write the final exam on May 16 (which will be primarily based on material covered in the homework assignments), or submit a singly-authored final project on a topic that is pre-approved by the instructor. Approval due date: Apr 19. Project due date: May 16. Final grade will be based approximately 50% on the homework and 50% on the final project or final exam.

Class Mailing List
If you are not already a member of the class mailing list, please join the list. (Please join the list if you are planning to attend the class, whether or not you are taking it for credit.) There are two steps to joining the list; the first is to follow the instructions on the web page (including picking a password), and the second is to REPLY TO the confirmation message sent to you by the system. This list will be used for important announcements. You can also send questions or comments to this list yourself (contact me if you have questions about when this is appropriate).

Another Class Offered This Semester
You may want to consider also taking Professor Carlos Fernandez-Granda's class Optimization-Based Data Analysis. The topics covered by the two courses are quite complementary.