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  • 1
    Electronic Resource
    Electronic Resource
    On stationary points of the implicit Lagrangian for nonlinear complementarity problems (1995)
    Springer
    Journal of optimization theory and applications 84 (1995), S. 653-663 
    Details
    ISSN: 1573-2878
    Keywords: Nonlinear complementarity problems ; implicit Lagrangians ; equivalent differentiable optimization problems ; stationary points ; descent methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Mangasarian and Solodov have recently introduced an unconstrained optimization problem whose global minima are solutions of the nonlinear complementarity problem (NCP). In this paper, we show that, if the mapping involved in NCP has a positive-definite Jacobian, then any stationary point of the optimization problem actually solves NCP. We also discuss a descent method for solving the unconstrained optimization problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02191990
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Unconstrained Optimization Reformulations of Variational Inequality Problems (1997)
    Springer
    Journal of optimization theory and applications 92 (1997), S. 439-456 
    Details
    ISSN: 1573-2878
    Keywords: Variational inequality problems ; unconstrained optimization reformulations ; global error bounds ; descent methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Recently, Peng considered a merit function for the variational inequality problem (VIP), which constitutes an unconstrained differentiable optimization reformulation of VIP. In this paper, we generalize the merit function proposed by Peng and study various properties of the generalized function. We call this function the D-gap function. We give conditions under which any stationary point of the D-gap function is a solution of VIP and conditions under which it provides a global error bound for VIP. We also present a descent method for solving VIP based on the D-gap function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022660704427
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    Paper (German National Licenses)
    Fulltext
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