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  • Nonlinear complementarity problems  (2)
  • unconstrained optimization reformulations  (2)
  • 31C15  (1)
  • 1
    Digitale Medien
    Digitale Medien
    On (r, 2)-capacities for a class of elliptic pseudo differential operators (1992)
    Springer
    Mathematische Annalen 293 (1992), S. 343-348 
    Details
    ISSN: 1432-1807
    Schlagwort(e): 60J45 ; 31C15 ; 35S99
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01444719
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  • 2
    Digitale Medien
    Digitale Medien
    Unconstrained Optimization Reformulations of Variational Inequality Problems (1997)
    Springer
    Journal of optimization theory and applications 92 (1997), S. 439-456 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Variational inequality problems ; unconstrained optimization reformulations ; global error bounds ; descent methods
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1022660704427
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  • 3
    Digitale Medien
    Digitale Medien
    New NCP-Functions and Their Properties (1997)
    Springer
    Journal of optimization theory and applications 94 (1997), S. 115-135 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Nonlinear complementarity problems ; NCP-functions ; merit functions ; unconstrained optimization reformulations ; error bounds ; bounded level sets
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Recently, Luo and Tseng proposed a class of merit functions for the nonlinear complementarity problem (NCP) and showed that it enjoys several interesting properties under some assumptions. In this paper, adopting a similar idea to that of Luo and Tseng, we present new merit functions for the NCP, which can be decomposed into component functions. We show that these merit functions not only share many properties with the one proposed by Luo and Tseng but also enjoy additional favorable properties owing to their decomposable structure. In particular, we present fairly mild conditions under which these merit functions have bounded level sets.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1022659603268
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  • 4
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): Nonlinear complementarity problems ; implicit Lagrangians ; equivalent differentiable optimization problems ; stationary points ; descent methods
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02191990
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