Key Information
About the content
This course will cover the very basic ideas in optimization. Topics include the basic theory and algorithms behind linear and integer linear programming along with some of the important applications. We will also explore the theory of convex polyhedra using linear programming.
Syllabus
Introductory Material
- Introduction to Linear Programming.
- The Diet Problem.
- Linear Programming Formulations.
- Tutorials on using GLPK (AMPL), Matlab, CVX and Microsft Excel.
- The Simplex Algorithm (basics).
- Handling unbounded problems
- Degeneracy
- Geometry of Simplex
- Initializing Simplex.
- Cycling and the Use of Bland's rule.
- Duality: dual variables and dual linear program.
- Strong duality theorem.
- Complementary Slackness.
- KKT conditions for Linear Programs.
- Understanding the dual problem: shadow costs.
- Extra: The revised simplex method.
- Advanced LP formulations: norm optimization.
- Least squares, and quadratic programming.
- Applications #1: Signal reconstruction and De-noising.
- Applications #2: Regression.
- Integer Linear Programming.
- Integer vs. Real-valued variables.
- NP-completeness: basic introduction.
- Reductions from Combinatorial Problems (SAT, TSP and Vertex Cover).
- Approximation Algorithms: Introduction.
- Branch and Bound Method
- Cutting Plane Method
- Applications: solving puzzles (Sudoku), reasoning about systems and other applications.
- Classification and Machine Learning
Instructors
- Shalom Ruben - Mechanical Engineering
- Sriram Sankaranarayanan - Department of Computer Science
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