An inertial proximal point method for difference of maximal monotone vector fields in Hadamard manifolds

João S. Andrade (), Jurandir de O. Lopes () and João Carlos de O. Souza ()
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João S. Andrade: Federal University of Piauí
Jurandir de O. Lopes: Federal University of Piauí
João Carlos de O. Souza: Federal University of Piauí

Journal of Global Optimization, 2023, vol. 85, issue 4, No 7, 968 pages

Abstract: Abstract We propose an inertial proximal point method for variational inclusion involving difference of two maximal monotone vector fields in Hadamard manifolds. We prove that if the sequence generated by the method is bounded, then every cluster point is a solution of the non-monotone variational inclusion. Some sufficient conditions for boundedness and full convergence of the sequence are presented. The efficiency of the method is verified by numerical experiments comparing its performance with classical versions of the method for monotone and non-monotone problems.

Keywords: Variational inclusion; Proximal point method; Monotone vector fields; DC functions; Hadamard manifolds; 65K05; 90C26; 90C48 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10898-022-01240-1

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