Open Access
Locating Objects in the Plane Using Global Optimization Techniques
Pierre Hansen,Rafael Blanquero,Emilio Carrizosa +2 more
- 01 Sep 2009
pp 1-31
16
TL;DR: This work addresses the problem of locating objects in the plane such as segments, arcs of circumferences, arbitrary convex sets, their complements or their boundaries, and yields a global optimization problem, whose resolution is dealt with using difference of convex (DC) techniques.
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Abstract: We address the problem of locating objects in the plane such as segments, arcs of circumferences, arbitrary convex sets, their complements or their boundaries. Given a set of points, we seek the rotation and translation for such an object optimizing a very general performance measure, which includes as a particular case the classical objectives in semi-obnoxious facility location. In general, the above-mentioned model yields a global optimization problem, whose resolution is dealt with using difference of convex (DC) techniques such as outer approximation or branch and bound.
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Citations
Visualizing data as objects by DC (difference of convex) optimization
TL;DR: This paper addresses the problem of visualizing in a bounded region a set of individuals, which has attached a dissimilarity measure and a statistical value, as convex objects as well as developing an algorithmic approach to visualize two real-world datasets.
Locating a semi-obnoxious covering facility with repelling polygonal regions
TL;DR: A finite dominating set of solutions is obtained, leading to a polynomial algorithm that protects a set of polygonal areas from the negative effects of a facility located in the Euclidean plane.
16
Location of Dimensional Facilities in a Continuous Space
TL;DR: In many cases, the facilities to be located cannot be represented by isolated points, but may be modeled as dimensional structures as mentioned in this paper, such as lines and circles in the plane and hyperplanes and hyperspheres in higher dimensional spaces.
15
A biobjective approach to recoverable robustness based on location planning
TL;DR: The idea of recoverable robustness requires that a solution can be recovered to a feasible one as soon as the realized scenario becomes known.
13
•Dissertation
Algorithms and Concepts for Robust Optimization
Marc Goerigk,Paul Scheidt +1 more
- 14 Jan 2013
TL;DR: The software library ROPI is presented as a framework for robust optimization with support for most established mixed-integer programming solvers with both theoretical and algorithmic aspects.
References
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A simplex method for function minimization
J. A. Nelder
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The DC (Difference of Convex Functions) Programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems
Le Thi Hoai An,Pham Dinh Tao +1 more
TL;DR: The computational efficiency of DCA suggests to us a deeper and more complete study on DC programming, using the special class of DC programs (when either g or h is polyhedral convex) called polyhedral DC programs.
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Convex Analysis and Global Optimization
Hoang Tuy
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TL;DR: This book presents state-of-the-art results and methodologies in modern global optimization, and has been a staple reference for researchers, engineers, advanced students, and practitioners in various fields of engineering.
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DC programming: overview
Reiner Horst,Nguyen Van Thoai +1 more
TL;DR: The purpose of this overview is to discuss main theoretical results, some applications, and solution methods for this interesting and important class of programming problems.
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