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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical programming 65 (1994), S. 43-72 
    ISSN: 1436-4646
    Keywords: Monotone complementarity problem ; Interior-point algorithm ; Potential reduction algorithm ; Infeasibility ; Global convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper presents a wide class of globally convergent interior-point algorithms for the nonlinear complementarity problem with a continuously differentiable monotone mapping in terms of a unified global convergence theory given by Polak in 1971 for general nonlinear programs. The class of algorithms is characterized as: Move in a Newton direction for approximating a point on the path of centers of the complementarity problem at each iteration. Starting from a strictly positive but infeasible initial point, each algorithm in the class either generates an approximate solution with a given accuracy or provides us with information that the complementarity problem has no solution in a given bounded set. We present three typical examples of our interior-point algorithms, a horn neighborhood model, a constrained potential reduction model with the use of the standard potential function, and a pure potential reduction model with the use of a new potential function.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical programming 43 (1989), S. 107-113 
    ISSN: 1436-4646
    Keywords: Complementarity problem ; continuation method ; P-function ; homeomorphism
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The complementarity problem with a nonlinear continuous mappingf from the nonnegative orthantR + n ofR n intoR n can be written as the system of equationsF(x, y) = 0 and(x, y) ∈ R + 2n , whereF denotes the mapping from the nonnegative orthantR + 2n ofR 2n intoR + n × Rn defined byF(x, y) = (x 1y1,⋯,xnyn, f1(x) − y1,⋯, fn(x) − yn) for every(x, y) ∈ R + 2n . Under the assumption thatf is a uniformP-function, this paper establishes that the mappingF is a homeomorphism ofR + 2n ontoR + n × Rn. This result provides a theoretical basis for a new continuation method of tracing the solution curve of the one parameter family of systems of equationsF(x, y) = tF(x 0, y0) and(x, y) ∈ R + 2n from an arbitrary initial point(x 0, y0) ∈ R + 2n witht = 1 until the parametert attains 0. This approach is an extension of the one used in the polynomially bounded algorithm recently given by Kojima, Mizuno and Yoshise for solving linear complementarity problems with positive semi-definite matrices.
    Type of Medium: Electronic Resource
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