Um algoritmo para funções DC em variedades de Hadamardusando aproximação de Yosida

João Santos Andrade, Jurandir de Oliveira Lopes, João Carlos de Oliveira Souza

Resumo


Baseando-se na aproximação de Yosida, apresentamos um algoritmo para encontrar pontos críticos de funções DC em variedades de Hadamard.  Mostramos que cada ponto de acumulação da sequência gerada por nosso algoritmo  ́e ponto crítico da função objetivo.


Texto completo:

PDF

Referências


Almeida, Y.T., Cruz Neto, J.X., Oliveira,P.R. and Souza, J.C.O. A modified proximal pointmethod for DC functions on Hadamard manifolds,Computational Optimization and Applica-tions, 76:649–673, 2020. DOI: 10.1007/s10589-020-00173-3.

Bento, G.C., Ferreira, O.P. and Melo. J.G. Iteration-Complexity of Gradient, Subgradientand Proximal Point Methods on Riemannian Manifolds,Journal of Optimization Theory andApplications, 173:548–562, 2017. DOI: 10.1007/s10957-017-1093-4.

Boumal,N.Anintroductiontooptimizationonsmoothmanifolds,2020.https://www.epfl.ch/schools/sb/education/sma/[4] Elhilali Alaoui, A. Caractrisation des fonctions D.C. (Characterization of D. C. functions),Ann. Sci. Math. Quebec, 20: 1-13, 1996.

Ferreira, O.P. and Oliveira, P.R. Proximal point algorithm on Riemannian manifolds,Opti-mization, 51:257-270, 2002. DOI:10.1080/02331930290019413.

Hiriart-Urruty, J.B. Generalized differentiabity, duality and optimization for problems dea-ling with difference of convex functions,Convexity and Duality in Optimization, 37-70, 1985.DOI:10.1007/978-3-642-45610-7−3.

Hiriart-Urruty, J.B. From convex optimization to nonconvex optimization. Necessary and suf-ficient conditions for global optimality,Nonsmooth Optimization and Related Topics, SpringerUS, chapter 13, pages 219-239, 1989.

Li, C., L ́opez, G., Mart ́ın-M ́arquez, V. and Wang, J. H. Resolvents of Set Valued MonotoneVector Fields in Hadamard Manifolds,Set-Valued and Variational Analysis, 19:361–383, 2011.DOI 10.1007/s11228-010-0169-1.

Moudafi, A. On critical points of the difference of two maximal monotone operators,AfrikaMatematika, 26:457–463, 2015. DOI 10.1007/s13370-013-0218-7.

Polyak, B.T.Introduction to Optimization. Optimization Software Inc., New York, 198.

Sakai, T.Riemannian Geometry. Translations of Mathematical Monographs, volume 149.American Mathematical Society, Providence, 1996.

Souza,J.C.O. and Oliveira,P.R. A proximal point method for DC functions on Hadamardmanifolds,Jornal of Global Optimization, 63:797-810, 2015. DOI:10.1007/s10898-015-0282-7.

Sun, W., Sampaio, R.J.B. and Candido, M.A.B. Proximal point algorithm for minimizationof DC Functions,Journal of Computational Mathematics, 21:451-462, 2003.




DOI: https://doi.org/10.5540/03.2021.008.01.0489

Apontamentos

  • Não há apontamentos.


SBMAC - Sociedade de Matemática Aplicada e Computacional
Edifício Medical Center - Rua Maestro João Seppe, nº. 900, 16º. andar - Sala 163 | São Carlos/SP - CEP: 13561-120
 


Normas para publicação | Contato