Math 515A: Fundamentals of Optimization

Terry Rockafellar

Winter 2001, Tuesday/Thursday 8:30-9:50
Optimization is concerned with a wide range of situations in which the maximum or minimum of a function is sought over some set specified by side conditions. It is one of the areas of modern mathematics in which "pure" and "applied" are most closely linked. There is continual interaction between computation, modeling, and frontier developments in analysis--called variational analysis--which are essential because classical analysis never was confronted with the issues that now arise.

This course (which is joint with AMATH 515 and INDE 515) covers the central ideas of optimization in mathematical modeling, problem formulation and classification, and the analysis of solutions and their properties. Some computational methods are studied, although that is more the province of 516 in the following quarter. The theme is the development of fundamental theory and the understanding of its motivations and uses.

Instead of a textbook, comprehensive lecture notes (previously written in TEX) will made available. Grades will be based on weekly homework assignments. There will be some work with computers, in terms of running existing software (Matlab) to get solutions in selected examples.

The course offers an unusual opportunity to experience the power of mathematical methodology in tackling difficult situations and making sense out of them, even if it means inventing new concepts to achieve the purpose. There aren't special prerequisites beyond "advanced calculus"; no one is expected to have studied optimization previously. (In particular 514 isn't required.) This is truly an introduction to the field.