Recent developments in linear programming. The course highlights advances in interior point methods and also addresses developments in the simplex method. Projective methods, including Karmarkar's original work, affine methods, and path-following methods, are examined. The relationships between these methods are discussed, as well as their relationships to methods in nonlinear programming. Also discussed are advances in data structures and other implementation issues.
Students have the opportunity to test software and solve large-scale linear programs.
An introduction to infinite dimensional optimization. An introduction to the use of nonlinear ordinary differential, difference and integral equations in modeling dynamic phenomena in engineering, the natural sciences, and the social sciences. Emphasis is on the art of constructing and solving very large-scale, complex dynamic models. Examples are drawn from operations research, environmental engineering, mathematical biology, economics, transportation, and other fields.