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Title of Journal: Mathematical Programming

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Abbravation: Mathematical Programming

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Springer Berlin Heidelberg

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DOI

10.1007/bf00336739

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1436-4646

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On the number of solutions to the linear compleme

Authors: Arie Tamir
Publish Date: 1976/12/01
Volume: 10, Issue: 1, Pages: 347-353
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Abstract

Given ann × n matrixA and anndimensional vectorq letNA q be the cardinality of the set of solutions to the linear complementarity problem defined byA andq It is shown that ifA is nondegenerate thenNA q + NA −q ⩽ 2 n which in turn impliesNA q ⩽ 2 n − 1 ifA is also aQmatrixIt is then demonstrated that min q≠0 NA q ⩽ 2 n−1 − 1 which concludes that the complementary cones cannot spanR n more than 2 n−1 − 1 times around For anyn an example of ann × n nondegenerateQmatrix spanning allR n but a subset of empty interior 2n/3 times around is given

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  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 robust and efficient method for solving point distance problems by homotopy
  14. A nonmonotone GRASP
  15. Extreme point inequalities and geometry of the rank sparsity ball
  16. Primal-dual interior-point methods for PDE-constrained optimization
  17. A new branch-and-cut algorithm for the capacitated vehicle routing problem
  18. Single item lot-sizing with non-decreasing capacities
  19. Structural and algorithmic properties for parametric minimum cuts
  20. Simple integer recourse models: convexity and convex approximations
  21. A model of the coNP-complete non-Hamilton tour decision problem for directed graphs
  22. Iteration complexity analysis of block coordinate descent methods
  23. Error Bounds of Regularized Gap Functions for Nonsmooth Variational Inequality Problems
  24. Accelerating the cubic regularization of Newton’s method on convex problems
  25. Bundle methods for sum-functions with “easy” components: applications to multicommodity network design
  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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