5,404 research outputs found
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 -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
Fairness in maximal covering location problems
Acknowledgments
The authors thank the anonymous reviewers and the guest editors
of this issue for their detailed comments on this paper, which provided
significant insights for improving the previous versions of this
manuscript.
This research has been partially supported by Spanish Ministerio
de Ciencia e Innovación, AEI/FEDER grant number PID2020-114594GB
C21, AEI grant number RED2022-134149-T (Thematic Network: Location
Science and Related Problems), Junta de AndalucÃa projects P18-
FR-1422/2369 and projects FEDERUS-1256951, B-FQM-322-UGR20,
CEI-3-FQM331 and NetmeetData (Fundación BBVA 2019). The first
author was also partially supported by the IMAG-Maria de Maeztu
grant CEX2020-001105-M /AEI /10.13039/501100011033 and UENextGenerationEU
(ayudas de movilidad para la recualificación del
profesorado universitario. The second author was also partially supported
by the Research Program for Young Talented Researchers of the
University of Málaga under Project B1-2022_37, Spanish Ministry of
Education and Science grant number PEJ2018-002962-A, and the PhD
Program in Mathematics at the Universidad de Granada.This paper provides a mathematical optimization framework to incorporate fairness measures from the facilities’ perspective to discrete and continuous maximal covering location problems. The main ingredients to construct a function measuring fairness in this problem are the use of (1) ordered weighted averaging operators, a popular family of aggregation criteria for solving multiobjective combinatorial optimization problems; and (2) -fairness operators which allow generalizing most of the equity measures. A general mathematical optimization model is derived which captures the notion of fairness in maximal covering location problems. The models are first formulated as mixed integer non-linear optimization problems for both the discrete and the continuous location spaces. Suitable mixed integer second order cone optimization reformulations are derived using geometric properties of the problem. Finally, the paper concludes with the results obtained from an extensive battery of computational experiments on real datasets. The obtained results support the convenience of the proposed approach.Spanish Ministerio
de Ciencia e InnovaciónAEI/FEDER grant number PID2020-114594GB
C21AEI grant number RED2022-134149-T (Thematic Network: Location
Science and Related Problems)Junta de AndalucÃa projects P18-
FR-1422/2369FEDERUS-1256951B-FQM-322-UGR20CEI-3-FQM331NetmeetData (Fundación BBVA 2019)IMAG-Maria de Maeztu
grant CEX2020-001105-M /AEI /10.13039/501100011033UE NextGenerationEUResearch Program for Young Talented Researchers of the
University of Málaga under Project B1-2022_37Spanish Ministry of
Education and Science grant number PEJ2018-002962-
A risk-aversion approach for the Multiobjective Stochastic Programming problem
Multiobjective stochastic programming is a field well located to tackle
problems arising in emergencies, given that uncertainty and multiple objectives
are usually present in such problems. A new concept of solution is proposed in
this work, especially designed for risk-aversion solutions. A linear
programming model is presented to obtain such solution.Comment: 29 pages, 3 figures, 17 table
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
Continuous multifacility ordered median location problems
In this paper we propose a general methodology for solving a broad class of continuous, multifacility location problems, in any dimension and with â„“Ï„ -norms proposing two different methodologies: 1) by a new second order cone mixed integer programming formulation and 2) by formulating a sequence of semidefinite programs that converges to the solution of the problem; each of these relaxed problems solvable with SDP solvers in polynomial time. We apply dimensionality reductions of the problems by sparsity and symmetry in order to be able to solve larger problems.
Continuous multifacility location and Ordered median problems and Semidefinite programming and Moment problem.Junta de AndalucÃaFondo Europeo de Desarrollo RegionalMinisterio de Ciencia e Innovació
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 â„“p 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 â„“p ordered median location problems in dimension d (including
of course the â„“p 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 AndalucÃaFondo Europeo de Desarrollo RegionalMinisterio de Ciencia e Innovació
- …