krylov subspaces – Optimization Online

An inexact alternating projection method with application to matrix completion

Published: 2025/05/11

Nonlinear Optimization, Other Topics affine rank minimization problems, alternating projections, inexact projections, krylov subspaces, matrix completion

We develop and analyze an inexact regularized alternating projection method for nonconvex feasibility problems. Such a method employs inexact projections on one of the two sets, according to a set of well-defined conditions. We prove the global convergence of the algorithm, provided that a certain merit function satisfies the Kurdyka-Lojasiewicz property on its domain. The … Read more

A shifted Steihaug-Toint method for computing a trust-region step.

Published: 2004/09/17

Ladislav Lukšan

Ctirad Matonoha

Jan Vlček

Unconstrained Optimization computational experiments, conjugate gradient method, krylov subspaces, large-scale optimization, trust-region methods, unconstrained optimization

Trust-region methods are very convenient in connection with the Newton method for unconstrained optimization. The More-Sorensen direct method and the Steihaug-Toint iterative method are most commonly used for solving trust-region subproblems. We propose a method which combines both of these approaches. Using the small-size Lanczos matrix, we apply the More-Sorensen method to a small-size trust-region … Read more