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An existence result on partitioning of a measurable space: Pareto optimality and core

Nobusumi Sagara (2006)

Kybernetika

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...

An existence theorem for extended mildly nonlinear complementarity problem in semi-inner product spaces

M. S. Khan (1995)

Commentationes Mathematicae Universitatis Carolinae

We prove a result for the existence and uniqueness of the solution for a class of mildly nonlinear complementarity problem in a uniformly convex and strongly smooth Banach space equipped with a semi-inner product. We also get an extension of a nonlinear complementarity problem over an infinite dimensional space. Our last results deal with the existence of a solution of mildly nonlinear complementarity problem in a reflexive Banach space.

An ex-post bound on the greedy heuristic for the uncapacitated facility location problem

Jean-Michel Thizy (2006)

RAIRO - Operations Research

A bound for the greedy heuristic applied to the K-facility location problem can be calculated, using values gathered during the calculation of the heuristic. The bound strengthens a well-known bound for the heuristic. Computational experiments show that this bound can be beneficial when the number of facilities is small or close to the total number of potential sites. In addition, it is consistent with previous results about the influence of the data characteristics upon the optimal value.

An extended version of average Markov decision processes on discrete spaces under fuzzy environment

Hugo Cruz-Suárez, Raúl Montes-de-Oca, R. Israel Ortega-Gutiérrez (2023)

Kybernetika

The article presents an extension of the theory of standard Markov decision processes on discrete spaces and with the average cost as the objective function which permits to take into account a fuzzy average cost of a trapezoidal type. In this context, the fuzzy optimal control problem is considered with respect to two cases: the max-order of the fuzzy numbers and the average ranking order of the trapezoidal fuzzy numbers. Each of these cases extends the standard optimal control problem, and for...

An extragradient iterative scheme by viscosity approximation methods for fixed point problems and variational inequality problems

Adrian Petruşel, Jen-Chih Yao (2009)

Open Mathematics

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.

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