Revisiting several problems and algorithms in continuous location with lp norms

This paper addresses the general continuous single facility location problems in finite dimension spaces under possibly different ℓp norms in the demand points. We analyze the difficulty of this family of problems and revisit convergence properties of some well-known algorithms. The ultimate goal is to provide a common approach to solve the family of continuous ℓp ordered median location problems in dimension d (including of course the ℓp minisum or Fermat-Weber location problem for any p ≥ 1). We prove that this approach has a polynomial worse case complexity for monotone lambda weights and can be also applied to constrained and even non-convex problems.Junta de AndalucíaFondo Europeo de Desarrollo RegionalMinisterio de Ciencia e Innovació

Efficient Methods for Automated Multi-Issue Negotiation: Negotiating over a Two-Part Tariff

In this article, we consider the novel approach of a seller and customer negotiating bilaterally about a two-part tariff, using autonomous software agents. An advantage of this approach is that win-win opportunities can be generated while keeping the problem of preference elicitation as simple as possible. We develop bargaining strategies that software agents can use to conduct the actual bilateral negotiation on behalf of their owners. We present a decomposition of bargaining strategies into concession strategies and Pareto-efficient-search methods: Concession and Pareto-search strategies focus on the conceding and win-win aspect of bargaining, respectively. An important technical contribution of this article lies in the development of two Pareto-search methods. Computer experiments show, for various concession strategies, that the respective use of these two Pareto-search methods by the two negotiators results in very efficient bargaining outcomes while negotiators concede the amount specified by their concession strategy

Improved results for the k-centrum straight-line location problem

The k-Centrum problem consists in finding a point that minimises the sum of the distances to the k farthest points out of a set of given points. It encloses as particular cases to two of the most known problems in Location Analysis: the center, also named as the minimum enclosing circle, and the median. In this paper the k-Centrum criteria is applied to obtaining a straight line-shaped facility. A reduced finite dominant set is determined and an algorithm with lower complexity than the previous one obtained.Ministerio de Ciencia y Tecnologí

A Semidefinite Programming approach for minimizing ordered weighted averages of rational functions

This paper considers the problem of minimizing the ordered weighted average (or ordered median) function of finitely many rational functions over compact semi-algebraic sets. Ordered weighted averages of rational functions are not, in general, neither rational functions nor the supremum of rational functions so that current results available for the minimization of rational functions cannot be applied to handle these problems. We prove that the problem can be transformed into a new problem embedded in a higher dimension space where it admits a convenient representation. This reformulation admits a hierarchy of SDP relaxations that approximates, up to any degree of accuracy, the optimal value of those problems. We apply this general framework to a broad family of continuous location problems showing that some difficult problems (convex and non-convex) that up to date could only be solved on the plane and with Euclidean distance, can be reasonably solved with different $\ell_p$-norms and in any finite dimension space. We illustrate this methodology with some extensive computational results on location problems in the plane and the 3-dimension space.Comment: 27 pages, 1 figure, 7 table

Navigating through a forest of quad trees to spot images in a database

This paper describes how we maintain color and spatial index information on more than 1,000,000 images and how we allow users to browse the spatial color feature space. We break down all our images in color-based quad trees and we store all quad trees in our main-memory database. We allow users to browse the quad trees directly, or they can pre-select images through our color bit vector, which acts as an index accelerator. A Java based textsc{gui is used to navigate through our image indexes

Lipschitz Adaptivity with Multiple Learning Rates in Online Learning

We aim to design adaptive online learning algorithms that take advantage of any special structure that might be present in the learning task at hand, with as little manual tuning by the user as possible. A fundamental obstacle that comes up in the design of such adaptive algorithms is to calibrate a so-called step-size or learning rate hyperparameter depending on variance, gradient norms, etc. A recent technique promises to overcome this difficulty by maintaining multiple learning rates in parallel. This technique has been applied in the MetaGrad algorithm for online convex optimization and the Squint algorithm for prediction with expert advice. However, in both cases the user still has to provide in advance a Lipschitz hyperparameter that bounds the norm of the gradients. Although this hyperparameter is typically not available in advance, tuning it correctly is crucial: if it is set too small, the methods may fail completely; but if it is taken too large, performance deteriorates significantly. In the present work we remove this Lipschitz hyperparameter by designing new versions of MetaGrad and Squint that adapt to its optimal value automatically. We achieve this by dynamically updating the set of active learning rates. For MetaGrad, we further improve the computational efficiency of handling constraints on the domain of prediction, and we remove the need to specify the number of rounds in advance.Comment: 22 pages. To appear in COLT 201

Finsler Active Contours

©2008 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.DOI: 10.1109/TPAMI.2007.70713In this paper, we propose an image segmentation technique based on augmenting the conformal (or geodesic) active contour framework with directional information. In the isotropic case, the euclidean metric is locally multiplied by a scalar conformal factor based on image information such that the weighted length of curves lying on points of interest (typically edges) is small. The conformal factor that is chosen depends only upon position and is in this sense isotropic. Although directional information has been studied previously for other segmentation frameworks, here, we show that if one desires to add directionality in the conformal active contour framework, then one gets a well-defined minimization problem in the case that the factor defines a Finsler metric. Optimal curves may be obtained using the calculus of variations or dynamic programming-based schemes. Finally, we demonstrate the technique by extracting roads from aerial imagery, blood vessels from medical angiograms, and neural tracts from diffusion-weighted magnetic resonance imagery