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Numerical Experience with a Class of Trust-Region Algorithms for Unconstrained Smooth Optimization

Abel Soares Siqueira(abel.s.siqueira***at***gmail.com)
Geovani Nunes Grapiglia(grapiglia***at***ufpr.br)

Abstract: In this paper we investigate the numerical performance of trust-region algorithms in which the trust-region radius is updated by a nonlinear rule according with the quality of the models. This class of algorithms fits into the Nonlinear Stepsize Control framework recently proposed by Toint (Optimization Methods and Software 28: 82–95, 2013). The nonlinear control of the trust-region radius is characterized by a pair (alpha, beta) of user-defined parameters. Notable particular cases are the standard trust-region algorithm and the Fan-Yuan trust-region algorithm, which are obtained, respectively, with the traditional choices (alpha, beta) = (1, 0) and (alpha, beta) = (1, 1). As expected, our numerical results show that the numerical behaviour in this class of trust-region algorithms can vary greatly with different choices for (alpha, beta). In particular, we have identified pairs of parameters which are more efficient than the traditional ones.

Keywords: Unconstrained Optimization, Trust-Region Algorithms and Algorithmic Parameters

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Category 2: Optimization Software and Modeling Systems (Optimization Software Benchmark )

Citation: Department of Mathematics, Federal University of Paraná, Curitiba, Paraná, Brazil. Nov/2016

Download: [PDF]

Entry Submitted: 11/11/2016
Entry Accepted: 11/11/2016
Entry Last Modified: 11/11/2016

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