An adaptive nonmonotone trust region algorithm. (4th March 2019)

• Record Type: Journal Article
• Authors: Rezaee, Saeed; Babaie-Kafaki, Saman
• Is Part Of: Optimization methods and software. Volume 34:Number 2(2019)
• Page Start: 264
• Page End: 277
• Publication Date: 2019-03-04
• Subjects: unconstrained optimization -- trust region method -- quasi-Newton update -- adaptive radius -- global convergence -- superlinear convergence; 65K05 -- 90C53 -- 49M37; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2017.1364738
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : Based on an eigenvalue analysis conducted on the scaled memoryless quasi-Newton updating formulas BFGS and DFP, an adaptive choice for the trust region radius is proposed. Then, using a trust region ratio obtained from a nonmonotone line search strategy, an adaptive nonmonotone trust region algorithm is developed. Under proper conditions, it is briefly shown that the proposed algorithm is globally and locally superlinearly convergent. Numerical experiments are done on a set of unconstrained optimization test problems of the CUTEr collection, using the Dolan–Moré performance profile. They show efficiency of the proposed algorithm.