An adaptive trust-region method without function evaluations

Geovani N. Grapiglia () and Gabriel F. D. Stella
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Geovani N. Grapiglia: Université catholique de Louvain, ICTEAM/INMA
Gabriel F. D. Stella: Universidade Federal do Paraná

Computational Optimization and Applications, 2022, vol. 82, issue 1, No 2, 60 pages

Abstract: Abstract In this paper we propose an adaptive trust-region method for smooth unconstrained optimization. The update rule for the trust-region radius relies only on gradient evaluations. Assuming that the gradient of the objective function is Lipschitz continuous, we establish worst-case complexity bounds for the number of gradient evaluations required by the proposed method to generate approximate stationary points. As a corollary, we establish a global convergence result. We also present numerical results on benchmark problems. In terms of the number of calls of the oracle, the proposed method compares favorably with trust-region methods that use evaluations of the objective function.

Keywords: Unconstrained optimization; Trust-region method; Global convergence; Worst-case complexity (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10589-022-00356-0

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