Error estimates for iterative algorithms for minimizing regularized quadratic subproblems. (3rd March 2020)

• Record Type: Journal Article
• Authors: Gould, Nicholas I. M.; Simoncini, Valeria
• Is Part Of: Optimization methods and software. Volume 35:Number 2(2020)
• Page Start: 304
• Page End: 328
• Publication Date: 2020-03-03
• Subjects: Trust-region subproblem -- regularized quadratic suubproblem -- error estimates -- Krylov subspace; 90C30; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2019.1670177
• Languages: English
• ISSNs: 1055-6788

Abstract

ABSTRACT: We derive bounds for the objective errors and gradient residuals when finding approximations to the solution of common regularized quadratic optimization problems within evolving Krylov spaces. These provide upper bounds on the number of iterations required to achieve a given stated accuracy. We illustrate the quality of our bounds on given test examples.