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Title of Journal: J Glob Optim

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Abbravation: Journal of Global Optimization

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Springer US

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DOI

10.1016/0304-3940(80)90049-X

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1573-2916

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Rigorous filtering using linear relaxations

Authors: Ferenc Domes Arnold Neumaier
Publish Date: 2011/05/05
Volume: 53, Issue: 3, Pages: 441-473
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Abstract

This paper presents rigorous filtering methods for continuous constraint satisfaction problems based on linear relaxations designed to efficiently handle the linear inequalities coming from a linear relaxation of quadratic constraints Filtering or pruning stands for reducing the search space of constraint satisfaction problems Discussed are old and new approaches for rigorously enclosing the solution set of linear systems of inequalities as well as different methods for computing linear relaxations This allows custom combinations of relaxation and filtering Care is taken to ensure that all methods correctly account for rounding errors in the computations The methods are implemented in the GloptLab environment for solving quadratic constraint satisfaction problems Demonstrative examples and tests comparing the different linear relaxation methods are also presented

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Other Papers In This Journal:
  1. On Slater’s condition and finite convergence of the Douglas–Rachford algorithm for solving convex feasibility problems in Euclidean spaces
  2. Iterative algorithms for variational inequality and equilibrium problems with applications
  3. Efficient Nash equilibria on semilattices
  4. Global optimal solutions to a class of quadrinomial minimization problems with one quadratic constraint
  5. Global search perspectives for multiobjective optimization
  6. Necessary optimality conditions for a set-valued fractional extremal programming problem under inclusion constraints
  7. On the image space analysis for vector quasi-equilibrium problems with a variable ordering relation
  8. Low dimensional simplex evolution: a new heuristic for global optimization
  9. A biased random-key genetic algorithm to maximize the number of accepted lightpaths in WDM optical networks
  10. Variational inclusions problems with applications to Ekeland’s variational principle, fixed point and optimization problems
  11. A branch-and-bound multi-parametric programming approach for non-convex multilevel optimization with polyhedral constraints
  12. Existence and iterative algorithm of solutions for a class of bilevel generalized mixed equilibrium problems in Banach spaces
  13. Vector equilibrium problems with elastic demands and capacity constraints
  14. Stability Index Method for Global Minimization
  15. Dynamic sample budget allocation in model-based optimization
  16. On an elliptic Kirchhoff-type problem depending on two parameters
  17. Some constraint qualifications for quasiconvex vector-valued systems
  18. Optimization methodology assessment for the inlet velocity profile of a hydraulic turbine draft tube: part II—performance evaluation of draft tube model
  19. Global optimization of polynomial-expressed nonlinear optimal control problems with semidefinite programming relaxation
  20. A Lagrangian search method for the P -median problem
  21. Minimum vertex cover in ball graphs through local search
  22. Approximating zeros of monotone operators by proximal point algorithms
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