NON-INTERIOR CONTINUATION METHOD FOR COMPLEMENTARITY PROBLEMS IN ABSENCE OF STRICT COMPLEMENTARITY

Min Sun () and Zhen-Jun Shi ()
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Min Sun: Department of Mathematics and Information Science, Zaozhuang University, Zaozhuang, Shandong, 277160, P. R. China
Zhen-Jun Shi: College of Operations Research and Management, Qufu Normal University, Rizhao, Shandong 276826, P. R. China;

Asia-Pacific Journal of Operational Research (APJOR), 2006, vol. 23, issue 01, 107-122

Abstract: In this paper, by using a modified smoothing function, we propose a new continuation method for complementarity problems withR0-function andP0-function in the absence of strict complementarity. At each iteration, the continuation method solves one linear system of equations and performs one line search. When the underlying mapping is both aP0-function and aR0-function and its Hessian is Lipschitz continuous, we prove the global convergence of the new method. The new method also has global Q-linear and local Q-quadratical convergence rates under the same conditions.

Keywords: Complementarity problem; P0-function; R0-function; path following; non-interior method; interior-point method (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:wsi:apjorx:v:23:y:2006:i:01:n:s0217595906000838

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DOI: 10.1142/S0217595906000838

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