|Grading and Exams|
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 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 Distributionally Robust Decisioning and Learning, Economic/Game Equilibrium, Online Pricing and Resource Allocation, Financial Techniques and Risk Management, Sparse and Low Rank Regression, Conic 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.
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 background 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. .