IEOR 262B: Mathematical Programming II

Professor Javad Lavaei, UC Berkeley

Instructor: Javad Lavaei
Time: Tuesdays and Thursdays, 12:30-2pm
Location: 3107 Etcheverry
TA: Han Feng (han_feng AT berkeley.edu)
Instructor's Office Hours: Thursdays, 2-3pm (4121 Etcheverry)
TA's Office Hours: Fridays, 12-1pm (4176A Etcheverry)
Grading Policy:

15% homework
40% (take-home) midterm exam (March 21)
45% project

Description

This course provides a fundamental understanding of general nonlinear optimization theory, convex optimization, conic optimization, low-rank optimization, numerical algorithms, and distributed computation. Some of the topics covered in this course are as follows:

Nonlinear optimization: First- and second-order conditions, Fritz John optimality conditions, Lagrangian, duality, augmented Lagrangian, exact penalty methods, inexact penalty methods, etc.
Convexity: Convex sets, convex functions, convex optimization, conic optimization, convex reformulations, etc.
Convexification: Low-rank optimization, conic relaxations, sum-of-squares, hierarchies for mixed-integer problems, etc.
Algorithms: Descent algorithms, conjugate gradient methods, gradient projection & conditional gradient methods, block coordinate methods, proximal methods, ADMM, interior point algorithms, second-order methods, accelerated methods, decomposition and distributed algorithms, convergence analysis, etc.
Applications: Machine learning, data science, etc.

Textbook

“Nonlinear Programming” by Dimitri P. Bertsekas, Athena Scientific, 3rd Edition.

“Linear and Nonlinear Programming” by David Luenberger and Yinyu Ye, Springer, 4th Edition.

“Convex Optimization” by Stephen Boyd and Lieven Vandenberghe, Cambridge University Press, 2004 (click here to download the book).

‘‘Low-Rank Semidefinite Programming: Theory and Applications" by Alex Lemon, Anthony Man-Cho So and Yinyu Ye, Foundations and Trends in Optimization, 2015 (click here to download the monograph).

Homework

Homework 4 (due on April 22 at 5pm)