CPLEX quadratic simplex?

Does anybody know which simplex-like algorithm CPLEX uses to solve quadratic programs. what is the开发者_如何学编程 so called Quadratic Simplex it is using?

Thank you in advance, Mehdi

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.