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On Minimizing and Stationary Sequences of a New Class of Merit Functions for Nonlinear Complementarity Problems

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  • H. D. Qi

Abstract

Motivated by the work of Fukushima and Pang (Ref. 1), we study the equivalent relationship between minimizing and stationary sequences of a new class of merit functions for nonlinear complementarity problems (NCP). These merit functions generalize that obtained via the squared Fischer–Burmeister NCP function, which was used in Ref. 1. We show that a stationary sequence {xk} ⊂ /Ren is a minimizing sequence under the condition that the function value sequence {F(x k)} is bounded above or the Jacobian matrix sequence {F′(x k)} is bounded, where F is the function involved in NCP. The latter condition is also assumed by Fukushima and Pang. The converse is true under the assumption of {F′(x k)} bounded. As an example shows, even for a bounded function F, the boundedness of the sequence {F′(x k)} is necessary for a minimizing sequence to be a stationary sequence.

Suggested Citation

  • H. D. Qi, 1999. "On Minimizing and Stationary Sequences of a New Class of Merit Functions for Nonlinear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 102(2), pages 411-431, August.
    • Handle: RePEc:spr:joptap:v:102:y:1999:i:2:d:10.1023_a:1021788625806
    DOI: 10.1023/A:1021788625806
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    1. O. L. Mangasarian, 1993. "Mathematical Programming in Neural Networks," INFORMS Journal on Computing, INFORMS, vol. 5(4), pages 349-360, November.
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