Structured matrices in unconstrained minimization methods

Authors:
Carmine Di Fiore
Affiliations:
Dipartimento Di Matematica, Università Di Roma "Tor Vergata", Roma, Italy
Venue:
Contemporary mathematics
Year:
2001

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Abstract

Structured matrix algebras L and a generalized BFGS-type iterative scheme have been recently exploited to introduce low complexity quasi-Newton methods, named LQN, for solving general (nonstructured) minimization problems. In this paper we study the inverse LQN methods, which define inverse Hessian approximations by an inverse BFGS-type updating procedure. As the known LQN, the inverse LQN methods can be implemented with only O(n log n) arithmetic operations per step and O(n) memory allocations. Moreover, they turn out to be particularly useful in the study of conditions on L which guarantee the extension of the fast BFGS local convergence properties to LQN-type algorithms.