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Title of Journal: Math Program

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Abbravation: Mathematical Programming

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Springer Berlin Heidelberg

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DOI

10.1007/bf03049044

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1436-4646

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A robust and efficient method for solving point di

Authors: Rémi Imbach Pascal Mathis Pascal Schreck
Publish Date: 2016/08/18
Volume: 163, Issue: 1-2, Pages: 115-144
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Abstract

The goal of Point Distance Solving Problems is to find 2D or 3D placements of points knowing distances between some pairs of points The common guideline is to solve them by a numerical iterative method eg Newton–Raphson method A sole solution is obtained whereas many exist However the number of solutions can be exponential and methods should provide solutions close to a sketch drawn by the user Geometric reasoning can help to simplify the underlying system of equations by changing a few equations and triangularizing it This triangularization is a geometric construction of solutions called construction plan We aim at finding several solutions close to the sketch on a onedimensional path defined by a global parameterhomotopy using a construction plan Some numerical instabilities may be encountered due to specific geometric configurations We address this problem by changing onthefly the construction plan Numerical results show that this hybrid method is efficient and robust

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  1. Submodular maximization meets streaming: matchings, matroids, and more
  2. Some computationally relevant group theoretic structures of fixed charge problems
  3. Applications of convex analysis within mathematics
  4. Large-scale semidefinite programs in electronic structure calculation
  5. A distributionally robust perspective on uncertainty quantification and chance constrained programming
  6. The factorization approach to large-scale linear programming
  7. Beyond symmetric Broyden for updating quadratic models in minimization without derivatives
  8. A spatial branch-and-cut method for nonconvex QCQP with bounded complex variables
  9. Breakpoint searching algorithms for the continuous quadratic knapsack problem
  10. Sandwich games
  11. Approximations of Nash equilibria
  12. Using cuts for mixed integer knapsack sets to generate cuts for mixed integer polyhedral conic sets
  13. A nonmonotone GRASP
  14. Extreme point inequalities and geometry of the rank sparsity ball
  15. Primal-dual interior-point methods for PDE-constrained optimization
  16. A new branch-and-cut algorithm for the capacitated vehicle routing problem
  17. Single item lot-sizing with non-decreasing capacities
  18. Structural and algorithmic properties for parametric minimum cuts
  19. Simple integer recourse models: convexity and convex approximations
  20. A model of the coNP-complete non-Hamilton tour decision problem for directed graphs
  21. Iteration complexity analysis of block coordinate descent methods
  22. Error Bounds of Regularized Gap Functions for Nonsmooth Variational Inequality Problems
  23. Accelerating the cubic regularization of Newton’s method on convex problems
  24. Bundle methods for sum-functions with “easy” components: applications to multicommodity network design
  25. On the number of solutions to the linear comple-mentarity problem
  26. Time-consistent approximations of risk-averse multistage stochastic optimization problems
  27. PEBBL: an object-oriented framework for scalable parallel branch and bound
  28. PEBBL: an object-oriented framework for scalable parallel branch and bound
  29. The capacitated max k -cut problem
  30. Critical extreme points of the 2-edge connected spanning subgraph polytope
  31. Nash equilibria in the two-player kidney exchange game
  32. On some properties and an application of the logarithmic barrier method
  33. Complementarity systems in optimization
  34. On the exact separation of mixed integer knapsack cuts
  35. Analysis of infeasible-interior-point paths arising with semidefinite linear complementarity problems
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