A new approach to variable metric algorithms

1970/03/01 by R. Fletcher · 76 citations
Mathematics · Computer Science · #Advanced Optimization Algorithms Research #Metaheuristic Optimization Algorithms Research #Optimization and Variational Analysis

paper · pdf · doi:10.1093/comjnl/13.3.317

Abstract

An approach to variable metric algorithms has been investigated in which the linear search sub-problem no longer becomes necessary. The property of quadratic termination has been replaced by one of monotonic convergence of the eigenvalues of the approximating matrix to the inverse hessian. A convex class of updating formulae which possess this property has been established, and a strategy has been indicated for choosing a member of the class so as to keep the approximation away from both singularity and unboundedness. A FORTRAN program has been tested extensively with encouraging results.

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