Modified Jacobian smoothing method for nonsmooth complementarity problems

Pin-Bo Chen (), Peng Zhang (), Xide Zhu () and Gui-Hua Lin ()
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Pin-Bo Chen: Shanghai University
Peng Zhang: Chongqing University of Posts and Telecommunications
Xide Zhu: Shanghai University
Gui-Hua Lin: Shanghai University

Computational Optimization and Applications, 2020, vol. 75, issue 1, No 8, 207-235

Abstract: Abstract This paper is devoted to solving a nonsmooth complementarity problem where the mapping is locally Lipschitz continuous but not continuously differentiable everywhere. We reformulate this nonsmooth complementarity problem as a system of nonsmooth equations with the max function and then propose an approximation to the reformulation by simultaneously smoothing the mapping and the max function. Based on the approximation, we present a modified Jacobian smoothing method for the nonsmooth complementarity problem. We show the Jacobian consistency of the function associated with the approximation, under which we establish the global and fast local convergence for the method under suitable assumptions. Finally, to show the effectiveness of the proposed method, we report our numerical experiments on some examples based on MCPLIB/GAMSLIB libraries or network Nash–Cournot game is proposed.

Keywords: Nonsmooth complementarity problem; Jacobian consistency; Jacobian smoothing method; Convergence; Network Nash–Cournot game; 90C30; 90C33; 90C56 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10589-019-00136-3

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