Microsoft Excel 2000 Solver uses the Generalized Reduced Gradient (GRG2) algorithm for optimizing nonlinear problems. This algorithm was developed by Leon Lasdon, of the University of Texas at Austin, and Allan Waren, of Cleveland State University.
Linear and integer problems use the simplex method, with bounds on the variables and the branch and bound method, implemented by John Watson and Dan Fylstra, of Frontline Systems, Inc.
Here's a description from authors.
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