A New Proof for Global Convergence of a Smoothing Homotopy Method for the Nonlinear Complementarity Problem

Xiaona Fan and Qinglun Yan ()
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Xiaona Fan: School of Science, Nanjing University of Posts and Telecommunications, Nanjing, Jiangsu 210023, P. R. China
Qinglun Yan: School of Science, Nanjing University of Posts and Telecommunications, Nanjing, Jiangsu 210023, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2018, vol. 35, issue 04, 1-13

Abstract: In this paper, we propose a new proof for smoothing homotopy method based on the Fischer–Burmeister function to solve the nonlinear complementarity problem under a nonmonotone solution condition. Under this assumption condition imposed on the defined mapping F, global convergence of a smooth curve determined by the referred homotopy equation is established for almost all initial points in R+n and it is actually regarded as an interior point method. Besides, if the initial point is expanded to Rn, the global convergence of the homotopy method is ensured under a similar condition. The numerical results are reported and illustrate that the method is efficient for some nonlinear complementarity problems.

Keywords: Nonlinear complementarity problem; smoothing homotopy method; smoothing function; global convergence (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1142/S0217595918500276

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