Descent methods with computational errors in Banach spaces. (2nd August 2020)

• Record Type: Journal Article
• Authors: Reich, Simeon; Zaslavski, Alexander J.
• Is Part Of: Optimization. Volume 69:Number 7/8(2020)
• Page Start: 1439
• Page End: 1450
• Publication Date: 2020-08-02
• Subjects: Banach space -- complete metric space -- convex function -- descent method -- iterative process; 49M37 -- 90C25 -- 90C30; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1576178
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: Given a Lipschitz convex and coercive objective function on a Banach space, we revisit the class of regular vector fields introduced in our previous work on descent methods. Taking into account computational errors, we study the behaviour of the values of the objective function for the process generated by a regular vector field and show that if the computational errors are small enough, then the values of the objective function become close to its infimum.