On the worst-case complexity of nonlinear stepsize control algorithms for convex unconstrained optimization. (3rd May 2016)

• Record Type: Journal Article
• Authors: Grapiglia, G.N.; Yuan, J.; Yuan, Y.
• Is Part Of: Optimization methods and software. Volume 31:Number 3(2016)
• Page Start: 591
• Page End: 604
• Publication Date: 2016-05-03
• Subjects: worst-case complexity -- trust-region methods -- regularization methods -- unconstrained optimization; 90C30 -- 65K05 -- 49M37 -- 49M15 -- 90C29; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2015.1130129
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : A Nonlinear Stepsize Control (NSC) framework has been proposed by Toint [ Nonlinear stepsize control, trust regions and regularizations for unconstrained optimization, Optim.Methods Softw. 28 (2013), pp. 82–95] for unconstrained optimization, generalizing many trust-region and regularization algorithms. More recently, worst-case complexity bounds for the generic NSC framework were proved by Grapiglia et al. [ On the convergence and worst-case complexity of trust-region and regularization methods for unconstrained optimization, Math. Program. 152 (2015), pp. 491–520] in the context of non-convex problems. In this paper, improved complexity bounds are obtained for convex and strongly convex objectives.