IEOR 262B: Mathematical Programming II

Professor Javad Lavaei, UC Berkeley

Instructor: Javad Lavaei
Time: Tuesdays and Thursdays, 12:30-2pm
Location: Online
Instructor's Office Hours: Thursdays, 2-3pm
Grading Policy:

15% homework
40% midterm exam (April 13)
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, etc.
Convexity: Convex sets, convex functions, convex optimization, conic optimization, convex reformulations, etc.
Convexification: Low-rank optimization, conic relaxations, sum-of-squares, etc.
Algorithms: Descent algorithms, conjugate gradient methods, gradient projection & conditional gradient methods, block coordinate methods, proximal methods, 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).