Broyden.C File Reference

#include "NOX.H"
#include "NOX_Common.H"
#include "NOX_Utils.H"
#include "NOX_LAPACK_Group.H"


class  Broyden
 Interface to modified Broyden problem defined in Broyden.C. More...


int main ()
 Main subroutine of Broyden.C.

Detailed Description

This is an example of using NOX with the NOX::Solver::TensorBased tensor-Krylov method.

This test problem is a modified extension of the "Broyden Tridiagonal Problem" from Jorge J. More', Burton S. Garbow, and Kenneth E. Hillstrom, Testing Unconstrained Optimization Software, ACM TOMS, Vol. 7, No. 1, March 1981, pp. 14-41. The modification involves squaring the last equation fn(x) and using it in a homotopy-type equation.

The parameter "lambda" is a homotopy-type parameter that may be varied from 0 to 1 to adjust the ill-conditioning of the problem. A value of 0 is the original, unmodified problem, while a value of 1 is that problem with the last equation squared. Typical values for increasingly ill-conditioned problems might be 0.9, 0.99, 0.999, etc.

The standard starting point is x(i) = -1, but setting x(i) = 0 tests the selected global strategy.

Brett Bader, CU Boulder, 2002

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