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New multiplier method for solving linear complementarity problems
Ulji, CHEN Guoqing
Front. Math. China. 2006, 1 (3): 368-381.
https://doi.org/10.1007/s11464-006-0015-9
A new multiplier method for solving the linear complementarity problem LCP(q,M) is proposed. By introducing a Lagrangian of LCP(q,M), a new smooth merit function θ(χ, λ) for LCP(q,M) is constructed. Based on it, a simple damped Newton-type algorithm with multiplier self-adjusting step is presented. When M is a P-matrix, the sequence {θ(χk, λk)} (where {(χk, λk)} is generated by the algorithm) is globally linearly convergent to zero and convergent in a finite number of iterations if the solution is degenerate. Numerical results suggest that the method is highly effcient and promising.
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