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University of Colorado Boulder
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Linear and Integer Programming
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Introductory Material
Introduction to Linear Programming.
Week #1:
The Diet Problem.
Linear Programming Formulations.
Tutorials on using GLPK (AMPL), Matlab, CVX and Microsft Excel.
The Simplex Algorithm (basics).
Week #2:
Handling unbounded problems
Degeneracy
Geometry of Simplex
Initializing Simplex.
Cycling and the Use of Bland's rule.
Week #3:
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.
Week #4:
Advanced LP formulations: norm optimization.
Least squares, and quadratic programming.
Applications #1: Signal reconstruction and De-noising.
Applications #2: Regression.
Week #5:
Integer Linear Programming.
Integer vs. Real-valued variables.
NP-completeness: basic introduction.
Reductions from Combinatorial Problems (SAT, TSP and Vertex Cover).
Approximation Algorithms: Introduction.
Week #6:
Branch and Bound Method
Cutting Plane Method
Week #7:
Applications: solving puzzles (Sudoku), reasoning about systems and other applications.
Classification and Machine Learning
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