DYNAMIC PROGRAMMING AND ASSOCIATED TOPICS

COMPSCI/ISYE/MATH 425

Focuses on optimization problems over discrete structures, such as shortest paths, spanning trees, flows, matchings, and the traveling salesman problem. We will investigate structural properties of these problems, and we will study both exact methods for their solution, and approximation algorithms.

COMPSCI/ISYE 526

Review of linear programming. Polynomial time methods for linear programming. Quadratic programs and linear complementarity problems and related solution techniques. Solution sets and their continuity properties. Error bounds for linear inequalities and programs. Parallel algorithms for linear and quadratic programs.

ISYE 823

Subjects vary.

COMPSCI/ISYE 719

Stochastic programming is concerned with decision making in the presence of uncertainty, where the eventual outcome depends on a future random event. Topics include modeling uncertainty in optimization problems, risk measures, stochastic programming algorithms, approximation and sampling methods, and applications. Students are strongly encouraged to have knowledge of linear programming (e.g.,MATH/​COMP SCI/​I SY E/​STAT  525) and probability and statistics (e.g.,MATH/​STAT  431). Knowledge of integer optimization (MATH/​COMP SCI/​I SY E  728) is helpful, but not required.

ISYE 323

Basic techniques for modeling and optimizing deterministic systems with emphasis on linear programming. Computer solution of optimization problems. Applications to production, logistics, and service systems.