Lectures: 2 sessions / week, 1.5 hours / session
Recitations: 1 session / week, 1 hour / session
The course is a comprehensive introduction to the theory, algorithms and applications of integer optimization and is organized in five parts.
Discusses how to formulate integer optimization problems, how to enhance the formulations to improve the quality of relaxations, how to obtain ideal formulations, the duality of integer optimization and how to solve the resulting relaxations both practically and theoretically. It also gives insight on why integer optimization problems are difficult.
Treats robust discrete optimization. This is a tractable methodology to address problems under uncertainty.
Develops the theory of lattices, outlines ideas from algebraic geometry that have had an impact on integer optimization, and discusses the geometry of integer optimization. These lectures provide the building blocks for developing algorithms.
Develops cutting plane methods, enumerative and heuristic methods and approximation algorithms.
Treats mixed integer optimization. This is a practically significant area as real world problems have very often both continuous and discrete variables.
Grades will be determined by performance on the following requirements. Weights are approximate, and class participation is an important tie breaker.
|3-4||Methods to enhance formulations|
|10||Algorithms for solving relaxations|
|11||Robust discrete optimization|
|17-18||Cutting plane methods|
|24-25||Mixed integer optimization|