On maximal monotonicity of bifunctions on Hadamard manifolds

Neto, J. X. Cruz; Jacinto, Flávia M. O.; Soares, P. A.; Souza, João Carlos O.

doi:10.1007/s10898-018-0663-9

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Lee In 2015 [15]1

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“…Cruz Neto, Jacinto, Soares Jr., and Souza in 2018 [6] Abstract. We study some conditions for a monotone bifunction to be maximally monotone by using a corresponding vector field associated to the bifunction and vice versa.…”

Section: Lee In 2015 [15]mentioning

confidence: 99%

Riemannian manifolds are KKM spaces

Park¹

2019

Advances in the Theory of Nonlinear Analysis and Its Application

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Section: Lee In 2015 [15]mentioning

confidence: 99%

Riemannian manifolds are KKM spaces

Park¹

2019

Advances in the Theory of Nonlinear Analysis and Its Application

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“…For an approach on this issue in Hadamard manifolds see, for example, Colao et al (2012), where the authors considered the case where EP is associated to a monotone bifunction satisfying a certain coercivity condition. Cruz Neto et al (2018b), the authors establish existence of solutions to equilibrium problems in Hadamard manifolds by perturbing the equilibrium bifunction. An approach on the existence of solutions in the case where the equilibrium problem is of the type vectorial with variable order can be found in Batista et al (2016).…”

Section: Introductionmentioning

confidence: 99%

A new regularization of equilibrium problems on Hadamard manifolds: applications to theories of desires

Bento

Neto

Soares³

et al. 2021

Ann Oper Res

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In this paper, we introduce a new proximal algorithm for equilibrium problems on a genuine Hadamard manifold, using a new regularization term. We first extend recent existence results by considering pseudomonotone bifunctions and a weaker sufficient condition than the coer-civity assumption. Then, we consider the convergence of this proximal-like algorithm which can be applied to genuinely Hadamard manifolds and not only to specific ones, as in the recent literature. A striking point is that our new regularization term have a clear interpretation in a recent "variational rationality" approach of human behavior. It represents the resistance to change aspects of such human dynamics driven by motivation to change aspects. This allows us to give an application to the theories of desires, showing how an agent must escape to a succession of temporary traps to be able to reach, at the end, his desires.

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On maximal monotonicity of bifunctions on Hadamard manifolds

Cited by 2 publications

References 44 publications

Riemannian manifolds are KKM spaces

Riemannian manifolds are KKM spaces

A new regularization of equilibrium problems on Hadamard manifolds: applications to theories of desires

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