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  • 1
    Book
    Book
    ¬The¬ linear complementarity problem (1992)
    London u.a. :Academic Press,
    Details
    Title: ¬The¬ linear complementarity problem
    Author: Cottle, Richard W.
    Contributer: Pang Jong-Shi , Stone, Richard E.
    Publisher: London u.a. :Academic Press,
    Year of publication: 1992
    Pages: 762 S.
    Series Statement: Computer science and scientific computing
    Type of Medium: Book
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  • 2
    Electronic Resource
    Electronic Resource
    SOLUTION OF THE GENERAL MULTICOMMODITY SPATIAL EQUILIBRIUM PROBLEM BY VARIATIONAL AND COMPLEMENTARITY METHODS (1984)
    Oxford, UK : Blackwell Publishing Ltd
    Journal of regional science 24 (1984), S. 0 
    Details
    ISSN: 1467-9787
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1467-9787.1984.tb00811.x
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    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    On a class of least-element complementarity problems (1979)
    Springer
    Mathematical programming 16 (1979), S. 111-126 
    Details
    ISSN: 1436-4646
    Keywords: Least Element ; Linear Complementarity ; Quadratic Programs ; Special Structure ; Applications ; Computational Experience
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The present paper studies the linear complementarity problem of finding vectorsx andy inR + n such thatc + Dx + y ≧ 0,b − x ≧ 0 andx T (c + Dx + y) = y T (b − x) = 0 whereD is aZ-matrix andb 〉 0. Complementarity problems of this nature arise, for example, from the minimization of certain quadratic functions subject to upper and lower bounds on the variables. Two least-element characterizations of solutions to the above linear complementarity problem are established first. Next, a new and direct method to solve this class of problems, which depends on the idea of “least-element solution” is presented. Finally, applications and computational experience with its implementation are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582097
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Error bounds for analytic systems and their applications (1994)
    Springer
    Mathematical programming 67 (1994), S. 1-28 
    Details
    ISSN: 1436-4646
    Keywords: Error bound ; Analytic systems ; Karush—Kuhn—Tucker conditions ; Affine variational inequality ; Complementarity problem ; Integer feasibility problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Using a 1958 result of Lojasiewicz, we establish an error bound for analytic systems consisting of equalities and inequalities defined by real analytic functions. In particular, we show that over any bounded region, the distance from any vectorx in the region to the solution set of an analytic system is bounded by a residual function, raised to a certain power, evaluated atx. For quadratic systems satisfying certain nonnegativity assumptions, we show that this exponent is equal to 1/2. We apply the error bounds to the Karush—Kuhn—Tucker system of a variational inequality, the affine variational inequality, the linear and nonlinear complementarity problem, and the 0–1 integer feasibility problem, and obtain new error bound results for these problems. The latter results extend previous work for polynomial systems and explain why a certain square-root term is needed in an error bound for the (monotone) linear complementarity problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582210
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    A parametric linear complementarity technique for the computation of equilibrium prices in a single commodity spatial model (1981)
    Springer
    Mathematical programming 20 (1981), S. 81-102 
    Details
    ISSN: 1436-4646
    Keywords: Arc—arc Weighted Adjacency Matrix ; Computational Results ; Parametric Linear Complementarity ; Spatial Equilibrium Model ; Special-Purpose Algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper presents a parametric linear complementarity technique for the computation of equilibrium prices in a single commodity spatial model. We first reformulate the model as a linear complementarity problem and then apply the parametric principal pivoting algorithm for its solution. This reformulation leads to the study of an “arc—arc weighted adjacency matrix” associated with a simple digraph having weights on the nodes. Several basic properties of such a matrix are derived. Using these properties, we show how the parametric principal pivoting algorithm can be greatly simplified in this application. Finally, we report some computational experience with the proposed technique for solving some large problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01589334
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    A unification of two classes ofQ-matrices (1981)
    Springer
    Mathematical programming 20 (1981), S. 348-352 
    Details
    ISSN: 1436-4646
    Keywords: Class of Matrices ; Linear Complementarity Problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This note presents a class ofQ-matrices which includes Saigal's classN ofQ-matrices with negative principal minors and the classE of strictly semi-monotoneQ-matrices.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01589357
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    An equivalence between two algorithms for quadratic programming (1981)
    Springer
    Mathematical programming 20 (1981), S. 152-165 
    Details
    ISSN: 1436-4646
    Keywords: Column Generation ; Equivalence of Algorithms ; Quadratic Programming ; Simplicial Decomposition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper, we demonstrate that the Van de Panne—Whinston symmetric simplex method when applied to a certain implicit formulation of a quadratic program generates the same sequence of primal feasible vectors as does the Von Hohenbalken simplicial decomposition algorithm specialized to the same program. Such an equivalence of the two algorithms extends earlier results for a least-distance program due to Cottle—Djang.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01589342
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    Paper (German National Licenses)
    Fulltext
  • 8
    Electronic Resource
    Electronic Resource
    Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications (1990)
    Springer
    Mathematical programming 48 (1990), S. 161-220 
    Details
    ISSN: 1436-4646
    Keywords: Variational inequality ; complementarity ; fixed points ; Walrasian equilibrium ; traffic assignment ; network equilibrium ; spatial price equilibrium ; Nash equilibrium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Over the past decade, the field of finite-dimensional variational inequality and complementarity problems has seen a rapid development in its theory of existence, uniqueness and sensitivity of solution(s), in the theory of algorithms, and in the application of these techniques to transportation planning, regional science, socio-economic analysis, energy modeling, and game theory. This paper provides a state-of-the-art review of these developments as well as a summary of some open research topics in this growing field.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582255
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    Paper (German National Licenses)
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  • 9
    Electronic Resource
    Electronic Resource
    Parallel Newton methods for the nonlinear complementarity problem (1988)
    Springer
    Mathematical programming 42 (1988), S. 407-420 
    Details
    ISSN: 1436-4646
    Keywords: Nonlinear complementarity problem ; Newton method ; parallel computing ; synchronized and asynchronous methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper, we discuss how the basic Newton method for solving the nonlinear complementarity problem can be implemented in a parallel computation environment. We propose some synchronized and asynchronous Newton methods and establish their convergence.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01589414
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    Paper (German National Licenses)
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  • 10
    Electronic Resource
    Electronic Resource
    Convergence of splitting and Newton methods for complementarity problems: An application of some sensitivity results (1993)
    Springer
    Mathematical programming 58 (1993), S. 149-160 
    Details
    ISSN: 1436-4646
    Keywords: Locally upper Lipschitzian ; complementarity problems ; variational inequality ; splitting methods ; Newton's method ; solution stability ; matrix classes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper is concerned with two well-known families of iterative methods for solving the linear and nonlinear complementarity problems. For the linear complementarity problem, we consider the class of matrix splitting methods and establish, under a finiteness assumption on the number of solutions, a necessary and sufficient condition for the convergence of the sequence of iterates produced. A rate of convergence result for this class of methods is also derived under a stability assumption on the limit solution. For the nonlinear complementarity problem, we establish the convergence of the Newton method under the assumption of a “pseudo-regular” solution which generalizes Robinson's concept of a “strongly regular” solution. In both instances, the convergence proofs rely on a common sensitivity result of the linear complementarity problem under perturbation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581264
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    Paper (German National Licenses)
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