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Internet shopping optimization problem

Jacek Błażewicz, Mikhail Y. Kovalyov, Jędrzej Musiał, Andrzej P. Urbański, Adam Wojciechowski (2010)

International Journal of Applied Mathematics and Computer Science

A high number of Internet shops makes it difficult for a customer to review manually all the available offers and select optimal outlets for shopping. A partial solution to the problem is brought by price comparators which produce price rankings from collected offers. However, their possibilities are limited to a comparison of offers for a single product requested by the customer. The issue we investigate in this paper is a multiple-item multiple-shop optimization problem, in which total expenses...

Interpretación de los precios sombra en presencia de degeneración.

Teresa León, Vicente Liern (1996)

Qüestiió

El propósito de nuestro trabajo es analizar la interpretación económica de las variables duales como "precios sombra" cuando la solución posible básica óptima del problema de programación lineal es degenerada. Resolvemos algunos ejemplos que ilustran esta interpretación usando el programa LINDO. Finalmente planteamos una modificación a la propuesta de Gal (1986) para llevar a cabo el análisis de sensibilidad en presencia de degeneración.

Interpretation and optimization of the k -means algorithm

Kristian Sabo, Rudolf Scitovski (2014)

Applications of Mathematics

The paper gives a new interpretation and a possible optimization of the well-known k -means algorithm for searching for a locally optimal partition of the set 𝒜 = { a i ∈ ℝ n : i = 1 , ⋯ , m } which consists of k disjoint nonempty subsets π 1 , ⋯ , π k , 1 ≤ k ≤ m . For this purpose, a new divided k -means algorithm was constructed as a limit case of the known smoothed k -means algorithm. It is shown that the algorithm constructed in this way coincides with the k -means algorithm if during the iterative procedure no data points appear in the Voronoi diagram....

Interval linear regression analysis based on Minkowski difference – a bridge between traditional and interval linear regression models

Masahiro Inuiguchi, Tetsuzo Tanino (2006)

Kybernetika

In this paper, we extend the traditional linear regression methods to the (numerical input)-(interval output) data case assuming both the observation/measurement error and the indeterminacy of the input-output relationship. We propose three different models based on three different assumptions of interval output data. In each model, the errors are defined as intervals by solving the interval equation representing the relationship among the interval output, the interval function and the interval...

Interval matrices with Monge property

Martin Černý (2020)

Applications of Mathematics

We generalize the Monge property of real matrices for interval matrices. We define two classes of interval matrices with the Monge property---in a strong and a weak sense. We study the fundamental properties of both types. We show several different characterizations of the strong Monge property. For the weak Monge property, we give a polynomial description and several sufficient and necessary conditions. For both classes, we study closure properties. We further propose a generalization of an algorithm...

Interval valued bimatrix games

Milan Hladík (2010)

Kybernetika

Payoffs in (bimatrix) games are usually not known precisely, but it is often possible to determine lower and upper bounds on payoffs. Such interval valued bimatrix games are considered in this paper. There are many questions arising in this context. First, we discuss the problem of existence of an equilibrium being common for all instances of interval values. We show that this property is equivalent to solvability of a certain linear mixed integer system of equations and inequalities. Second, we...

Inverse modelling of image-based patient-specific blood vessels: zero-pressure geometry and in vivo stress incorporation

Joris Bols, Joris Degroote, Bram Trachet, Benedict Verhegghe, Patrick Segers, Jan Vierendeels (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In vivo visualization of cardiovascular structures is possible using medical images. However, one has to realize that the resulting 3D geometries correspond to in vivo conditions. This entails an internal stress state to be present in the in vivo measured geometry of e.g. a blood vessel due to the presence of the blood pressure. In order to correct for this in vivo stress, this paper presents an inverse method to restore the original zero-pressure geometry of a structure, and to recover the in vivo...

Inverse problem in engineering plasticity: a quadratic programming approach

Giulio Maier (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si considera un modello discreto (per elementi finiti) di un solido o un sistema strutturale perfettamente elastoplastico, con condizioni di snervamento «linearizzate a tratti», nell’ipotesi di olonomia assunta per processi di caricamento proporzionali. Supponendo noti su base sperimentale certi spostamenti sotto assegnate azioni esterne, si formula il problema di identificare i limiti di snervamento, ossia le resistenze locali. Si dimostra che questo problema inverso di meccanica strutturale non...

Iterative methods with analytical preconditioning technique to linear complementarity problems: application to obstacle problems

H. Saberi Najafi, S. A. Edalatpanah (2013)

RAIRO - Operations Research - Recherche Opérationnelle

For solving linear complementarity problems LCP more attention has recently been paid on a class of iterative methods called the matrix-splitting. But up to now, no paper has discussed the effect of preconditioning technique for matrix-splitting methods in LCP. So, this paper is planning to fill in this gap and we use a class of preconditioners with generalized Accelerated Overrelaxation (GAOR) methods and analyze the convergence of these methods for LCP. Furthermore, Comparison between our methods...

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