A derivative-free algorithm for spherically constrained optimization

Min Xi (), Wenyu Sun (), Yannan Chen () and Hailin Sun ()
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Min Xi: Nanjing Normal University
Wenyu Sun: Nanjing Normal University
Yannan Chen: South China Normal University
Hailin Sun: Nanjing Normal University

Journal of Global Optimization, 2020, vol. 76, issue 4, No 10, 861 pages

Abstract: Abstract Spherically constrained optimization, which minimizes an objective function on a unit sphere, has wide applications in numerical multilinear algebra, signal processing, solid mechanics, etc. In this paper, we consider a certain case that the derivatives of the objective function are unavailable. This case arises frequently in computational science, chemistry, physics, and other enormous areas. To explore the spherical structure of the above problem, we apply the Cayley transform to preserve iterates on the sphere and propose a derivative-free algorithm, which employs a simple model-based trust-region framework. Under mild conditions, global convergence of the proposed algorithm is established. Preliminary numerical experiments illustrate the promising performances of our algorithm.

Keywords: Derivative-free optimization; Spherically constrained optimization; Simple model; Trust-region method; Global convergence (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10898-020-00875-2

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