An effective adaptive trust region algorithm for nonsmooth minimization



In this paper, an adaptive trust region algorithm that uses Moreau–Yosida regularization is proposed for solving nonsmooth unconstrained optimization problems. The proposed algorithm combines a modified secant equation with the BFGS update formula and an adaptive trust region radius, and the new trust region radius utilizes not only the function information but also the gradient information. The global convergence and the local superlinear convergence of the proposed algorithm are proven under suitable conditions. Finally, the preliminary results from comparing the proposed algorithm with some existing algorithms using numerical experiments reveal that the proposed algorithm is quite promising for solving nonsmooth unconstrained optimization problems.


Nonsmooth problems Moreau–Yosida regularization Trust region algorithm Global convergence Superlinear convergence 

Mathematical subject classification

65K05 90C26 



The authors would like to thank the referees and the editor for their valuable comments that greatly improved this paper. This work is supported by the National Natural Science Foundation of China (11661009 and 11261006), the Guangxi Science Fund for Distinguished Young Scholars (No. 2015GXNSFGA139001), the Guangxi Natural Science Key Fund (No. 2017GXNSFDA198046), and the Basic Ability Promotion Project of Guangxi Young and Middle-aged Teachers (No. 2017KY0019).


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Mathematics and Information ScienceGuangxi UniversityNanningPeople’s Republic of China

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