An adaptive nonmonotone trust region algorithm

An improved nonmonotone adaptive trust region method

“…We compare the AINATR method with the ANMTR method [18] and the RNATR method [16]. In the numerical experiments, the following parameters are used in the AINATR method:…”

“…and M 1 is a given nonnegative integer. Many authors [20], [23], [7], [18] generalized the Grippo's nonmonotone term into the adaptive trust region framework and obtained good numerical results. Peyghami and Tarzanagh [16] provided a new adaptive trust region algorithm which incorporates a variant of nonmonotone technique.…”

“…Under mild conditions, we analyze the global convergence and superlinear convergence of the proposed method. Numerical results show that for the CUTEr library and the test problem collection given by Andrei [3], the proposed method is superior to the adaptive methods in [16], [18].…”

A randomized nonmonotone adaptive trust region method based on the simulated annealing strategy for unconstrained optimization

“…Here, we report the results obtained by applying MATLAB 7.14.0.739 (R2012a) runs of Algorithm 1 (MANMTR), Algorithm 2 (RANMTR) and the nonmonotone adaptive TR algorithm suggested by (Shi and Wang, 2011), here called NMATR. The implementations were executed on a set of 90 test functions of CUTEr (Gould et al, 2003) with the minimum dimension 50 (selected based on the considerations of (Hager and Zhang, 2006;Rezaee and Babaie-Kafaki, 2019)), as specified in Table I, using a computer Intel(R) Core(TM)2 Duo CPU 2.00 GHz with 1.50 GB of RAM.…”

“…The literature contains justifiable studies on the radii and the ratios of the TR methods; (see, e.g. Rezaee and Babaie-Kafaki, 2018;Rezaee and Babaie-Kafaki, 2019;Yuan, 2015 and the references therein).…”