Two iterative processes generated by regular vector fields in Banach spaces. (3rd April 2022)

• Record Type: Journal Article
• Authors: Reich, Simeon; Zaslavski, Alexander J.
• Is Part Of: Optimization. Volume 71:Number 4(2022)
• Page Start: 779
• Page End: 789
• Publication Date: 2022-04-03
• Subjects: Banach space -- complete metric space -- convex function -- descent method -- iterative process; 49M37 -- 90C25 -- 90C30; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1865348
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : Given a convex objective function on a Banach space, which is Lipschitz on bounded sets, we consider the class of regular vector fields introduced in our previous work on descent methods. We analyze the behaviour of the values of the objective function for two iterative processes generated by a regular vector field in the presence of computational errors and show that if the computational errors tend to zero, then the values of the objective function converge to its infimum.