Structured matrix algebras L and a generalized BFGS-type iterative scheme have been recently investigated to introduce low-complexity quasi-Newton methods, named LQN, for solving general (non-structured) minimization problems. In this paper we introduce the LkQN 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.
DI FIORE, C., Fanelli, S., Zellini, P. (2005). Low-complexity minimization algorithms. NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 12, 755-768 [10.1002/nla.449].
Low-complexity minimization algorithms
DI FIORE, CARMINE;FANELLI, STEFANO;ZELLINI, PAOLO
2005-01-01
Abstract
Structured matrix algebras L and a generalized BFGS-type iterative scheme have been recently investigated to introduce low-complexity quasi-Newton methods, named LQN, for solving general (non-structured) minimization problems. In this paper we introduce the LkQN 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.| File | Dimensione | Formato | |
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