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Smoothing power penalty method for nonlinear complementarity problems. (English) Zbl 1343.90098
Summary: We introduce a new penalty method for solving nonlinear complementarity problems, which unifies the existing \(\ell_1\)-penalty method and the natural residual equation-based method. We establish the exponential convergence rate between a solution of the penalized equations and that of the complementarity problem under a uniform \(\xi\)-\(P\)-function and study a perturbed \(b\)-regularity condition. Two kinds of numerical algorithms with global and fast local convergence are designed by virtue of the proposed penalty method.
Preliminary numerical experiments conducted on test problems from Software: MATLAB; TRESNEI; MCPLIB show that the proposed method is efficient and robust.
MSC:
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
65K15 Numerical methods for variational inequalities and related problems
49M30 Other numerical methods in calculus of variations (MSC2010)
Software:
Matlab; MCPLIB; TRESNEI
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