On the cyclic pseudomonotonicity and the proximal point algorithm

Hadi Khatibzadeh; Vahid Mohebbi; Mohammad Hossein Alizadeh

doi:10.3934/naco.2018027

Article Contents

2018, Volume 8, Issue 4: 441-449. Doi: 10.3934/naco.2018027

This issue Previous Article Optimization problems with orthogonal matrix constraints Next Article Quantitative stability analysis of stochastic mathematical programs with vertical complementarity constraints

On the cyclic pseudomonotonicity and the proximal point algorithm

1.
Department of Mathematics, University of Zanjan, P. O. Box 45195-313, Zanjan, Iran
2.
Department of Mathematics, Institute for Advanced Studies in Basic Sciences, P. O. Box 45195-1159, Zanjan, Iran

^* Corresponding author
^* Corresponding author

Received: June 2017

Revised: August 2018

Published: September 2018

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Abstract

We introduce various versions of cyclic pseudomonotonicity and study the relations between them. Some examples about the relation between them and monotonicity are also presented. By imposing some assumptions on the cyclic pseudomonotone bifunctions, we study the convergence analysis of the proximal point algorithm which has been studied by Iusem and Sosa [5] for pseudomonotone bifunctions, with better assumptions.

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Mathematics Subject Classification: 90C33, 65K15.

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