| General Information
| Course Outline
- Class Times and Locations
- Class Room: NVIDIA Auditorium
- Lectures Time: Mondays and Wednesdays 11:30 AM - 12:50; and
- Extra Session (Problem Session, Project Session, Make-Up Lectures): Selected Fridays 11:30 AM - 12:50 (decided in advance)
for Q&A and Discussions.
- Prerequisites : Math 113, 115 (or equivalent).
- Text: David Luenberger and Yinyu Ye, Linear and Nonlinear Programming, 4th Edition. See also Handouts for supplemental text.
- Office: Huang 308
- Office hours: Wednesdays 1:00 - 2:30 (Check the announcement site for any possible change), or by appointment
- Email: firstname.lastname@example.org
- Phone: 723-7262
- Course Assistant: Adrea Zanette
- Office: Huang Basement
- Office hours: Tuesday 6pm-7pm
- Email: email@example.com
- Course Assistant: Sergio Gomez
- Office: Huang Basement
- Office hours: Monday 4:30-5:30pm
- Email: firstname.lastname@example.org
- Course Assistant: Junzi Zhang
- Office: Huang Basement
- Office hours: Wednesday 5-6pm
- Email: email@example.com
- Staff Support: Roz Morf
- Office: Huang 339A
- Email: firstname.lastname@example.org
- Phone: 723-4173
- Homework Exercises:
4 homework assignments, -- 40%.
A team project (up to 4 people) due March 20, -- 30%
- Final Examination:
March 24 in class (there would be an alternative date for justfied request), -- 30%
CME307/MS&E311 emphasizes high level pictues of (convex or nonconvex) Optimization, including classical duality theories, KKT conditions, efficient algorithms and recent progresses in Linear and Nonlinear Optimization---one of the central mathematical decision models in Data Science, Business Analytics, and Operations Management. CME307MS&E311 can be viewed as a continuation course of MS&E211. Although there are some minor overlaps with MS&E 211, CME307/MS&E311 covers more advanced application models, in-depth optimization theories, and state of the art algorithms which were not able to be covered by MS&E211.
CME307/MS&E311 also extensively covers nonlinear and nonconvex optimization problems, complementing to MS&E310 (Linear Optimization) and other "Convex Optimization" courses.
The field of optimization is
concerned with the study of maximization and minimization of mathematical
functions. Very often the arguments of (i.e., variables in) these functions are
subject to side conditions or constraints. By virtue of its great utility in such diverse areas as applied science, engineering, economics, finance, medicine, data analysis, machine learning and statistics, optimization holds an important place in both the
practical world and the scientific world. Indeed, as far back as the Eighteenth
Century, the famous Swiss mathematician and physicist Leonhard Euler
(1707-1783) proclaimed that ... nothing at all takes place in the Universe
in which some rule of maximum or minimum does not appear. The subject is so
pervasive that we even find some optimization terms in our everyday language.
Optimization is so large a subject that it cannot
adequately be treated in the short amount time available in one quarter of an
academic year. In this course, we shall restrict our attention mainly to some
aspects of nonlinear programming and discuss linear programming as a special
case. Among the many topics that will not be covered in this course are
integer programming, network programming, and stochastic programming.
Optimization often goes by the name Mathematical
Programming (MP). The latter name tends to be used in conjunction with
finite-dimensional optimization problems, which in fact are what we shall be
studying here. The word "Programming" should not be confused with
computer programming which in fact it antedates. As originally used, the term
refers to the timing and magnitude of actions to be carried out so as to
achieve a goal in the best possible way. Highlights of topics are Prediction Markets, Economic/Game Equilibrium, (Online) Pricing and Resource Allocation Models, Financial Decision and Risk Management, Sparse and Low Rank Opimization, Conic Linear Optimization, Steepest Descent Method, Accelerated Descent, BCD methods, SGD methods, ADMM methods, Interior-Point Methods, Lagrangian relaxations, Optimization with random samplings and column generation, etc,, which you would learn during the process of the course.
Question, Comments and Suggestions: If you have any comments or suggestions on lectures, recitation
sessi$sessions or any other issures, you can send us messages via Piazza.
What background is needed for CME307/MS&E311?
This is a graduate-level Core course in the ICME and MS&E Department.
No prior optimization background is required (although it should do no
harm to have some). In this sense, it is an introductory course,
but it is not intended to be an elementary course. Students who have
taken courses such as MS&E 211 (or MS&E 310) will see some
repetition of material. This is unavoidable, but CME 307 and MS&E 311 are intended
to be more theoretical than MS&E 211.
Students in this course will be expected to possess a firm
in the following mathematical subjects: multivariate differential
calculus; fundamental concepts of analysis; linear
algebra and matrix theory. Familiarity with computers
and computer programming are also be useful, since various algorithm implementation projects can be substituted for the final exam. Above all, it is essential
to have a tolerance for
mathematical discourse plus an ability to follow - and devise one's own
- mathematical proofs. .