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. Mathematical Programming is one of the central quantitative decision models in Management Science and Operations Research. Highlights of topics are Information Aggregation, Economic Equilibrium, Pricing Model, Core of Game, Financial Decision and Risk Management, Sparse and Low Rank Opimization and its Computations, which you would learn during the process of the course.
What background is needed for MS&E 311? This is an advanced master or doctoral-level Core course in the 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 MS&E 311 is intended to be more theoretical and advanced than MS&E 211.
Students in this course will be expected to possess a firm background in the following mathematical subjects: multivariate differential calculus; basic concepts of analysis; linear algebra and some matrix theory. Familiarity with computers and computer programming might also be useful. Above all, it is essential to have a tolerance for mathematical discourse plus an ability to follow - and sometimes devise one's own - mathematical proofs. These play a much larger role in the course than computer work.