IEOR 262B: Mathematical Programming II

Instructor: Javad Lavaei
Time: Tuesdays and Thursdays, 12:30-2pm
Location: 3107 Etcheverry
TA: Han Feng (han_feng AT
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


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.


  • “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 1

Homework 2

Homework 3

Midterm Exam

Homework 4 (due on April 22 at 5pm)