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  • 1
    Electronic Resource
    Electronic Resource
    The (n + 1)2 m -ray algorithm: a new simplicial algorithm for the variational inequality problem on ℝ + m ×S n (1993)
    Springer
    Annals of operations research 44 (1993), S. 93-113 
    Details
    ISSN: 1572-9338
    Keywords: Variational inequality problem ; nonlinear complementarity problem ; simplicial algorithm ; triangulation ; piecewise linear approximation ; convergence condition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract In this paper we propose a variable dimension simplicial algorithm for solving the variational inequality problem on the cross product of the nonnegative orthant ℝ + m of them-dimensional Euclidean space ℝ m and then-dimensional unit simplexS n of ℝ n+1. Starting from an arbitrary point (u, v) єℝ + m ×S n, the algorithm generates a piecewise linear path in ℝ + m ×S n. The path is traced by making alternately linear programming pivot operations and replacement steps in an appropriate simplicial subdivision of ℝ + m ×S n. The algorithm differs from the thus far known algorithm in the number of directions in which it may leave the starting point. More precisely, the algorithm has (n+1)2 m rays to leave the starting point whereas the existing algorithm hasn+m+1 rays. A convergence condition is presented and the accuracy estimation of an approximate solution generated is also given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02073592
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A continuous deformation algorithm for variational inequality problems on polytopes (1994)
    Springer
    Mathematical programming 64 (1994), S. 103-122 
    Details
    ISSN: 1436-4646
    Keywords: Variational inequality ; Stationary point ; Simplicial algorithm ; Variable dimension algorithm ; Continuous deformation ; Triangulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A continuous deformation algorithm is proposed for solving a variational inequality problem on a polytopeK. The algorithm embeds the polytopeK intoK× [0, ∞) and starts by applying a variable dimension algorithm onK× {0} until an approximate solution is found onK× {0}. Then by tracing the path of solutions of a system of equations the algorithm virtually follows a path of approximate solution inK× [0, ∞). When the path inK× [0, ∞) returns to level 0, i.e.,K× {0}, the variable dimension algorithm is again used until a new approximate solution is found onK× {0}. The setK× [0, ∞) is triangulated so that the approximate solution on the path improves the accuracy as the level increases. A contrivance for a practical implementation of the algorithm is proposed and tested for some test problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582567
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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