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list 7 sequences
assignment Level : Intermediate
chat_bubble_outline Language : English
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credit_card Free access
verified_user Free certificate
timer 35 hours in total

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.

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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


  • Shalom Ruben - Mechanical Engineering
  • Sriram Sankaranarayanan - Department of Computer Science

Content Designer

University of Colorado Boulder

The University of Colorado at Boulder is an American university located in Boulder (Colorado).

The university was founded in 1870, six years after the creation of the state of Colorado. It was built on a 30-hectare site. In 1872, the campus was enlarged to 80 hectares.




Coursera is a digital company offering massive open online course founded by computer teachers Andrew Ng and Daphne Koller Stanford University, located in Mountain View, California. 

Coursera works with top universities and organizations to make some of their courses available online, and offers courses in many subjects, including: physics, engineering, humanities, medicine, biology, social sciences, mathematics, business, computer science, digital marketing, data science, and other subjects.

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