Set-Valued Var. Anal

2015

DOI: 10.1007/s11228-015-0343-6

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Some Conditions for Maximal Monotonicity of Bifunctions

Nicolas Hadjisavvas

¹

,

Flávia M. O. Jacinto

²

,

Juan Enrique Martínez-Legaz

³

Abstract: We present necessary and sufficient conditions for a monotone bifunction to be maximally monotone, based on a recent characterization of maximally monotone operators. These conditions state the existence of solutions to equilibrium problems obtained by perturbing the defining bifunction in a suitable way.

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Bifunctions and Saddle Functions1

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Cited by 5 publications

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“…The converse is not true: A F may be monotone while F is not. See [8] for examples, and Proposition 6 below.…”

Section: Bifunctions and Saddle Functionsmentioning

confidence: 99%

Representative functions of maximally monotone operators and bifunctions

¹

,

²

,

³

2016

Math. Program.

Self Cite

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The aim of this paper is to show that every representative function of a maximal monotone operator is the Fitzpatrick transform of a bifunction corresponding to the operator. In this way we exhibit the relation between the recent theory of representative functions, and the much older theory of saddle functions initiated by Rockafellar.

“…The converse is not true: A F may be monotone while F is not. See [8] for examples, and Proposition 6 below.…”

Section: Bifunctions and Saddle Functionsmentioning

confidence: 99%

Representative functions of maximally monotone operators and bifunctions

¹

,

²

,

³

2016

Math. Program.

Self Cite

View full text Add to dashboard Cite

The aim of this paper is to show that every representative function of a maximal monotone operator is the Fitzpatrick transform of a bifunction corresponding to the operator. In this way we exhibit the relation between the recent theory of representative functions, and the much older theory of saddle functions initiated by Rockafellar.

Augmented Lagrangian methods for optimal control problems governed by mixed quasi‐equilibrium problems with applications

¹

,

²

,

³

2021

Optim Control Appl Methods

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The main goal of this article is to study a general augmented Lagrangian method for optimal control problems governed by mixed (quasi-)equilibrium problems.We establish zero duality gap properties between a primal problem and its augmented Lagrangian dual problem. As a consequence, we give some existence results for optimal control problem governed by evolutionary quasi-variational inequalities. An application to optimal control of obstacle problems described by quasi-hemivariational inequalities is studied. The results obtained in this article are new and improves considerably many recent results in literature. K E Y W O R D Saugmented Lagrangian methods, mixed quasi-equilibrium problems, Mosco convergence, optimal control problems, quasi-hemivariational inequalities, quasi-variational inequalities

On maximal monotonicity of bifunctions on Hadamard manifolds

¹

,

²

,

³

et al. 2018

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