Low‐complexity minimization algorithms

Abstract

Abstract Structured matrix algebras ℒ︁ and a generalized BFGS‐type iterative scheme have been recently investigated to introduce low‐complexity quasi‐Newton methods, named ℒ︁QN, for solving general (non‐structured) minimization problems. In this paper we introduce the ℒ︁ k QN methods, which exploit ad hoc algebras at each step. Since the structure of the updated matrices can be modified at each iteration, the new methods can better fit the Hessian matrix, thereby improving the rate of convergence of the algorithm. Copyright © 2005 John Wiley & Sons, Ltd.