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The existence of solutions to a scalar Minty variational inequality of differential type is usually related to monotonicity property of the primitive function. On the other hand, solutions of the variational inequality are global minimizers for the primitive function.
The present paper generalizes these results to vector variational inequalities
putting the Increasing Along Rays (IAR) property into the center of the discussion. To achieve that infinite elements in the image space Y are introduced.
Under...
Soit F une famille de critères conçue pour asseoir un modèle de préférences global sur un ensemble A d'actions potentielles (ou alternatives). On se place ici dans une perspective d'aide à la décision et dans l'hypothèse où des dépendances (encore
appelées interactions) sont susceptibles d'exister entre certains des critères de F. On commence (cf. Sect. 2.1) par préciser ce que signifie
l'affirmation "il existe des dépendances entre certains des critères de F" (Déf. 1). On s'intéresse ensuite...
We present a regularization method to approach a solution of the pessimistic formulation of ill-posed bilevel problems. This allows to overcome the difficulty arising from the non uniqueness of the lower level problems solutions and responses. We prove existence of approximated solutions, give convergence result using Hoffman-like assumptions. We end with objective value
error estimates.
We consider a decision-making problem to evaluate absolute ratings of alternatives that are compared in pairs according to two criteria, subject to box constraints on the ratings. The problem is formulated as the log-Chebyshev approximation of two pairwise comparison matrices by a common consistent matrix (a symmetrically reciprocal matrix of unit rank), to minimize the approximation errors for both matrices simultaneously. We rearrange the approximation problem as a constrained bi-objective optimization...
In the present paper a complete procedure for solving Multiple Objective Integer Linear Programming Problems is presented. The algorithm can be regarded as a corrected form and an alternative to the method that was proposed by Gupta and Malhotra. A numerical illustration is given to show that this latter can miss some efficient solutions. Whereas, the algorithm stated bellow determines all efficient solutions without missing any one.
In the present paper a complete procedure for solving Multiple
Objective Integer Linear Programming Problems is presented. The algorithm
can be regarded as a corrected form and an alternative to the method that
was proposed by Gupta and Malhotra. A numerical illustration is given to
show that this latter can miss some efficient solutions. Whereas, the
algorithm stated bellow determines all efficient solutions without
missing any one.
This paper investigates the problem of optimal partitioning of a measurable space among a finite number of individuals. We demonstrate the sufficient conditions for the existence of weakly Pareto optimal partitions and for the equivalence between weak Pareto optimality and Pareto optimality. We demonstrate that every weakly Pareto optimal partition is a solution to the problem of maximizing a weighted sum of individual utilities. We also provide sufficient conditions for the existence of core partitions...
In this paper, we introduce a new iterative process for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for an α-inverse-strongly-monotone, by combining an modified extragradient scheme with the viscosity approximation method. We prove a strong convergence theorem for the sequences generated by this new iterative process.
This paper considers the problem of robust reconstruction of simultaneous actuator and sensor faults for a class of uncertain Takagi-Sugeno nonlinear systems with unmeasurable premise variables. The proposed fault reconstruction and estimation design method with H∞ performance is used to reconstruct both actuator and sensor faults when the latter are transformed into pseudo-actuator faults by introducing a simple filter. The main contribution is to develop a sliding mode observer (SMO) with two...
Partiendo del problema de programación lineal multiobjetivo bajo incertidumbre y definiendo la utilidad de una decisión factible x, como el k-ésimo valor ordenado del vector (c1x, c2x, ..., cpx), estudiamos en este trabajo el problema múltiple planteado en el caso de un conocimiento incompleto de los objetivos, así como la sensibilidad de una solución óptima en relación con dicho conocimiento parcial.
En este trabajo se estudian procedimientos para la elección entre las soluciones eficientes del Problema de Programación Lineal con Objetivos Múltiples, cuando el decisor manifiesta preferencias sobre ciertas ordenaciones de las valoraciones de las funciones objetivo, utilizándose como criterio de valoración global funciones basadas en el k-ésimo valor del vector de los objetivos ordenado en cada punto.Se desarrollan procedimientos para generar ordenaciones compatibles con la información del decisor....
This paper provides a convergent numerical approximation of the Pareto optimal set for finite-horizon multiobjective optimal control problems in which the objective space is not necessarily convex. Our approach is based on Viability Theory. We first introduce a set-valued return function V and show that the epigraph of V equals the viability kernel of a certain related augmented dynamical system. We then introduce an approximate set-valued return function with finite set-values as the solution of...
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