The modified absolute-value factorization norm for trust-region minimization

A trust-region method for unconstrained minimization, using a trustregion norm based upon a modified absolute-value factorization of the model Hessian, is proposed. It is shown that the resulting trust-region subproblem may be solved using a single factorization. In the convex case, the method reduces to a backtracking Newton linesearch procedure. The resulting software package is available as HSL_VF06 within the Harwell Subroutine Library. Numerical evidence shows that the approach is effective in the nonconvex case.

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