This paper addresses a large class of vector optimization problems in infinite-dimensional spaces with respect to two important binary relations derived from domination structures. Motivated by theoretical challenges as well as by applications to some models in behavioral sciences, we establish new...
This paper has two parts. The mathematical part provides generalized versions of the robust Ekeland variational principle in terms of set-valued EVP with variable preferences, uncertain parameters and changing weights given to vectorial perturbation functions. The behavioural part that motivates our...
In this paper, in the context of quasi-metric spaces, we obtain two set-valued versions of the Ekeland variational-type principle by means of lower and upper set less relations, for the case where the perturbations need not satisfy the triangle inequality. An application in terms of migration proble...
We first give a pre-order principle whose form is very general. Combining the pre-order principle and generalized Gerstewitz functions, we establish a general equilibrium version of set-valued Ekeland variational principle (denoted by EVP), where the objective function is a set-valued bimap defined...
This paper has two aspects. Mathematically, in the context of global optimization, it provides the existence of an optimum of a perturbed optimization problem that generalizes the celebrated Ekeland variational principle and equivalent formulations (Caristi, Takahashi), whenever the perturbations ne...
Variational principles are very powerful tools when studying self-adjoint linear operators on a Hilbert space $\mathcal H$. Bounds for eigenvalues, comparison theorems, interlacing results, and monotonicity of eigenvalues can be proved easily with these characterizations, to name just a few. In this...
Étant donné l’engagement de Bergson pour une conception dynamique du temps et un avenir ouvert, il semble probable qu’il n’aurait pas accueilli favorablement les développements de la physique qui suggèrent que nous vivons dans un éternel univers de blocs à quatre dimensions. Au cours des dernières d...
By using a pre-order principle in [Qiu JH. A pre-order principle and set-valued Ekeland variational principle. J Math Anal Appl. 2014;419:904–937], we establish a general equilibrium version of set-valued Ekeland variational principle (denoted by EVP), where the objective function is a set-valued bi...
This paper is devoted to new versions of Ekeland’s variational principle in set optimization with domination structure, where set optimization is an extension of vector optimization from vector-valued functions to set-valued maps using Kuroiwa’s set-less relations to compare one entire image set wit...
This paper is written in honour of the centenary of Emmy Amalie Noether's famous article entitled Invariante Variationsprobleme. It firstly aims to give an exposition of what we believe to be the most significant and elegant issues regarding her theorems, through the lens of classical mechanics. Des...
Using a pre-order principle in [Qiu JH. A pre-order principle and set-valued Ekeland variational principle. J Math Anal Appl. 2014;419:904–937], we establish a general equilibrium version of set-valued Ekeland variational principle (denoted by EVP), where the objective bimap is defined on the produc...
This paper has a twofold focus. The mathematical aspect of the paper shows that new and existing quasimetric and weak r-distance versions of Ekeland’s variational principle are equivalent in the sense that one implies the other, and so are their corresponding fixed-point results. The practical aspec...
In this paper, driven by Behavioral applications to human dynamics, we consider the characterization of completeness in pseudo-quasimetric spaces in term of a generalization of Ekeland’s variational principle in such spaces, and provide examples illustrating significant improvements to some previous...
The paper is devoted to variational analysis of set-valued mappings acting from quasimetric spaces into topological spaces with variable ordering structures. Besides the mathematical novelty, our...
Le sens en mathématiques classiques est-il incompatible avec l’intuitionnisme ? Nous analysons le clivage classique/ intuitionniste, et la façon dont il est reflété dans les théories modernes des infinitésimaux. Lorsque l’intuitionniste Heyting annonça que «la création de l’analyse nonstandard est u...
Describing scientific change involves displaying scientific theories and their content. This is done by way of (rational) reconstructions, which usually neglect the variety of versions in which a scientific theory may appear. Although they possess a unity allowing them to bear the same name for deca...
In the present chapter, I sketch the history of this development, from the introduction of the first variational principles to the elaboration of Lagrange's "analytical mechanics". This is the history of the transformation of mechanics from a geometric science into an analytical one, or even, accord...
Cette deuxième communication apporte deux résultats supplémentaires : — la description de la dynamique de l'action des ondes dans des structures périodiques répond aux principes variationnels de la mécanique (formulation Hamiltonienne) — l'examen de la question de l'incertitude : les paquets d'ondes...
Variational formulations are proposed for the study of the hydrodynamic stability of an infinite fluid layer at rest heated from below. The role of a temperature dependent surface tension is more specifically emphasized. Both perturbations of small and finite amplitudes are considered : the former a...
The inter-relations among various approximate methods of solving the Boltzmann equation for the structure of a shock wave are discussed. It is shown that a certain class of moment methods and variational principles, including the local potential technique, have many desirable properties, and give th...
Les travaux récents de P. Glansdorff et T. Prigogine permettent d'étendre le domaine d'application de la Thermodynamique des Phénomènes Irréversibles aux processus loin de l'équilibre et incluant l'effet de grandeurs hydromagnétiques. L'objet de ce travail est de présenter l'inégalité fondamentale d...