MPI parallel programming of mixed integer optimization problems using CPLEX with COIN-OR

The aim of this technical report is to present some detailed explanations in order to help to understand and use the Message Passing Interface (MPI) parallel programming for solving several mixed integer optimization problems. We have developed a C++ experimental code that uses the IBM ILOG CPLEX optimizer within the COmputational INfrastructure for Operations Research (COIN-OR) and MPI parallel computing for solving the optimization models under UNIX-like systems. The computational experience illustrates how can we solve 44 optimization problems which are asymmetric with respect to the number of integer and continuous variables and the number of constraints. We also report a comparative with the speedup and efficiency of several strategies implemented for some available number of threads.

A Passage to India: from novel to film. Some problems of "translation"

Eguíluz, Federico; Merino, Raquel; Olsen, Vickie; Pajares, Eterio; Santamaría, José Miguel (eds.)

On a Class of Self-Adjoint Compact Operators in Hilbert Spaces and Their Relations with Their Finite-Range Truncations

This paper investigates a class of self-adjoint compact operators in Hilbert spaces related to their truncated versions with finite-dimensional ranges. The comparisons are established in terms of worst-case norm errors of the composite operators generated from iterated computations. Some boundedness properties of the worst-case norms of the errors in their respective fixed points in which they exist are also given. The iterated sequences are expanded in separable Hilbert spaces through the use of numerable orthonormal bases.

Adaptive Scalable SVD Unit for Fast Processing of Large LSE Problems

Singular Value Decomposition (SVD) is a key linear algebraic operation in many scientific and engineering applications. In particular, many computational intelligence systems rely on machine learning methods involving high dimensionality datasets that have to be fast processed for real-time adaptability. In this paper we describe a practical FPGA (Field Programmable Gate Array) implementation of a SVD processor for accelerating the solution of large LSE problems. The design approach has been comprehensive, from the algorithmic refinement to the numerical analysis to the customization for an efficient hardware realization. The processing scheme rests on an adaptive vector rotation evaluator for error regularization that enhances convergence speed with no penalty on the solution accuracy. The proposed architecture, which follows a data transfer scheme, is scalable and based on the interconnection of simple rotations units, which allows for a trade-off between occupied area and processing acceleration in the final implementation. This permits the SVD processor to be implemented both on low-cost and highend FPGAs, according to the final application requirements.

Problems when generating virtual models representing real objects: Hondarribia walls

[EN] This paper is based in the following project:

A common axiom for classical division rules for claims problems

In this paper we introduce a new axiom, denoted claims separability, that is satisfied by several classical division rules defined for claims problems. We characterize axiomatically the entire family of division rules that satisfy this new axiom. In addition, employing claims separability, we characterize the minimal overlap rule, given by O'Neill (1982), Piniles rule and the rules in the TAL-family, introduced by Moreno-Ternero and Villar (2006), which includes the uniform gains rule, the uniform losses rule and the Talmud rule.

Geodésicas en Variedades de Riemann

En este trabajo, se hará una introducción a las variedades de Riemann, con el fin de analizar algunas propiedades minimizadoras de las curvas geodésicas en variedades de Riemann.

On the optimal usage of labelled examples in semi-supervised multi-class classification problems

In recent years, the performance of semi-supervised learning has been theoretically investigated. However, most of this theoretical development has focussed on binary classification problems. In this paper, we take it a step further by extending the work of Castelli and Cover [1] [2] to the multi-class paradigm. Particularly, we consider the key problem in semi-supervised learning of classifying an unseen instance x into one of K different classes, using a training dataset sampled from a mixture density distribution and composed of l labelled records and u unlabelled examples. Even under the assumption of identifiability of the mixture and having infinite unlabelled examples, labelled records are needed to determine the K decision regions. Therefore, in this paper, we first investigate the minimum number of labelled examples needed to accomplish that task. Then, we propose an optimal multi-class learning algorithm which is a generalisation of the optimal procedure proposed in the literature for binary problems. Finally, we make use of this generalisation to study the probability of error when the binary class constraint is relaxed.

A potential approach to claims problems

Hart and Mas Colell (1989) introduce the potential function for cooperative TU games. In this paper, we extend this approach to claims problems, also known as bankruptcy or rationing problems. We show that for appropriate subproblems, the random arrival rule, the rules in the TAL-family (which include the uniform gains rule, the uniform losses rule and the Talmud rule), the minimal overlap rule, and the proportional rule admit a potential. We also study the balanced contributions property for these rules. By means of a potential, we introduce a generalization of the random arrival rule and mixtures of the minimal overlap rule and the uniform losses rule.

Instances of combinatorial optimization problems: complexity and generation

138 p.

Embedding quantum simulators

79 p.

Intuicionismo y formalismo en la filosofía de la matemática de I. Kant y H. Hilbert. Sobre función y significado de la intuición matemática

514 p.

Helmholtz Fermi surface harmonics: an efficient approach for treating anisotropic problems involving Fermi surface integrals

We present a new efficient numerical approach for representing anisotropic physical quantities and/or matrix elements defined on the Fermi surface (FS) of metallic materials. The method introduces a set of numerically calculated generalized orthonormal functions which are the solutions of the Helmholtz equation defined on the FS. Noteworthy, many properties of our proposed basis set are also shared by the FS harmonics introduced by Philip B Allen (1976 Phys. Rev. B 13 1416), proposed to be constructed as polynomials of the cartesian components of the electronic velocity. The main motivation of both approaches is identical, to handle anisotropic problems efficiently. However, in our approach the basis set is defined as the eigenfunctions of a differential operator and several desirable properties are introduced by construction. The method is demonstrated to be very robust in handling problems with any crystal structure or topology of the FS, and the periodicity of the reciprocal space is treated as a boundary condition for our Helmholtz equation. We illustrate the method by analysing the free-electron-like lithium (Li), sodium (Na), copper (Cu), lead (Pb), tungsten (W) and magnesium diboride (MgB2)

Ecuaciones integrales en el contexto de espacios de Hilbert

Las ideas básicas de la teoría de los espacios de Hilbert tienen como origen diversos problemas del análisis funcional, entre los cuales podemos citar los relativos a ciertas ecuaciones integrales lineales. Concretamente, un precedente de los métodos de la teoría espectral de operadores fue precisamente el enfoque de I. Fredholm de resolución de ciertas ecuaciones integrales mediante la teoría de matrices y determinantes infinitos utilizando el método de coeficientes indeterminados. Imitando la técnica de von Koch para desarrollar determinantes infinitos, Fredholm desarrolló su famoso teorema de alternativa en la resolución de las ecuaciones que llevan su nombre. Algunos tipos de ecuaciones integrales lineales están relacionados con operadores acotados completamente continuos y la teoría espectral para esta clase de operadores se podrá aplicar en la resolución de estas ecuaciones. En esta memoria se estudian distintos aspectos de estas y otras ecuaciones integrales. En el capítulo 1 se definen los conceptos básicos necesarios para el seguimiento de la misma, como es la de operador lineal y sus propiedades. Se distingue una clase importante de operadores, los compactos. Y se demuestra que todo operador integral pertenece a esta clase de operadores. En los capítulos 2 y 3 se introduce el concepto de ecuación integral, diferenciando las de Fredholm de las de Volterra, y se estudian diferentes técnicas de resolución de dichas ecuaciones, como son el teorema de alternativa, el teorema espectral para operadores compactos y autoadjuntos, ecuaciones integrales con núcleos degenerados y resolución por el método de aproximaciones sucesivas. Para finalizar, en el apéndice se resuelven algunos ejercicios utilizando los diferentes métodos estudiados.