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Does anybody know which simplex-like algorithm CPLEX uses to solve quadratic programs. what is the so called Quadratic Simplex it is using?

Thank you in advance, Mehdi

Mehdi
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1 Answers1

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I'm not sure what CPLEX uses but the Simplex Method has been modified by Philip Wolfe to solve quadratic programming. In a nut shell, this is what it does:

Given a quadratic programming problem: QPP. p'x + 1/2x'Cx with constrains Ax = b

  1. C has to be symmetric positive definite (positive semi-definite might work as well)
  2. generate linear constraints using the Karush-Kuhn-Tucker conditions
  3. modify the Simplex method in a way such that complementary slackness holds when choosing the pivot columns.
  4. proceed with the other usual Simplex method steps

For more detailed information, please take a look at this paper: http://pages.cs.wisc.edu/~brecht/cs838docs/wolfe-qp.pdf

Hope this helps.