The Difference of Convex Algorithm on Hadamard Manifolds

Ronny Bergmann (), Orizon P. Ferreira (), Elianderson M. Santos () and João Carlos O. Souza ()
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Ronny Bergmann: Norwegian University of Science and Technology
Orizon P. Ferreira: Federal University of Goiás
Elianderson M. Santos: Federal Institute of Education, Science and Technology of Maranhão
João Carlos O. Souza: Federal University of Piauí

Journal of Optimization Theory and Applications, 2024, vol. 201, issue 1, No 9, 251 pages

Abstract: Abstract In this paper, we propose a Riemannian version of the difference of convex algorithm (DCA) to solve a minimization problem involving the difference of convex (DC) function. The equivalence between the classical and simplified Riemannian versions of the DCA is established. We also prove that under mild assumptions the Riemannian version of the DCA is well defined and every cluster point of the sequence generated by the proposed method, if any, is a critical point of the objective DC function. Some duality relations between the DC problem and its dual are also established. To illustrate the algorithm’s effectiveness, some numerical experiments are presented.

Keywords: DC programming; DCA; Fenchel conjugate function; Riemannian manifolds; 90C30; 90C26; 49N14; 49Q99 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02392-8

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