Taiwanese Journal of Mathematics

AN INEXACT PROXIMAL POINT ALGORITHM FOR NONMONOTONE EQUILIBRIUM PROBLEMS IN BANACH SPACES

Guo-ji Tang and Xing Wang

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Abstract

In this paper, we continue to investigate the inexact hybrid proximal point algorithm proposed by Mashreghi and Nasri for equilibrium problems in Banach spaces. Under some classes of generalized monotone conditions, we prove that the sequence generated by the method is strongly convergent to a solution of the problem, which is closest to the initial iterate, in the sense of Bregman distance. As an application, we obtain some analogues for some classes of generalized monotone variational inequalities. The results presented in this paper generalize and improve some recent results in literatures.

Article information

Source
Taiwanese J. Math., Volume 17, Number 6 (2013), 2117-2133.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499706288

Digital Object Identifier
doi:10.11650/tjm.17.2013.3266

Mathematical Reviews number (MathSciNet)
MR3141877

Zentralblatt MATH identifier
1305.90387

Subjects
Primary: 90C30: Nonlinear programming 47H05: Monotone operators and generalizations

Keywords
proximal point algorithm strong convergence generalized monotonicity equilibrium problem variational inequality Banach space

Citation

Tang, Guo-ji; Wang, Xing. AN INEXACT PROXIMAL POINT ALGORITHM FOR NONMONOTONE EQUILIBRIUM PROBLEMS IN BANACH SPACES. Taiwanese J. Math. 17 (2013), no. 6, 2117--2133. doi:10.11650/tjm.17.2013.3266. https://projecteuclid.org/euclid.twjm/1499706288


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