A note on line search termination criteria for collinear scaling algorithms

Authors:
K. A. Ariyawansa;Wayne L. Tabor
Affiliations:
Department of Mathematics, Washington State University, Pullman, WA;Department of Mathematics, Washington State University, Pullman, WA
Venue:
Computing
Year:
2003

Citing 2
Cited 0

Deriving collinear scaling algorithms as extension of quasi-Newton methods and the local convergence of DFP-and BFGS-related collinear scaling algorithms

Mathematical Programming: Series A and B
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)

Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)

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Abstract

Ariyawansa [2] has introduced a line search termination criterion for collinear scaling minimization algorithms. However, he verified that this criterion provides sufficient decrease only in the case of objective functions that satisfy certain strong convexity assumptions. In this paper, we report results of our attempts to relax these assumptions. We present an example of a continuously differentiable, nonconvex function with bounded level sets on which the criterion of Ariyawansa [2] does not provide sufficient decrease. This example indicates that specifying line search termination criteria for collinear scaling algorithms is still an open problem. On a more positive note, we are able to show that the class of objective functions on which the criterion of Ariyawansa [2] provides sufficient decrease can be extended to include convex and strictly pseudo-convex functions.