Abstract
By introducing a smooth merit function for the median function, a new smooth merit function for box constrained variational inequalities (BVIs) was constructed. The function is simple and has some good differential properties. A damped Newton type method was presented based on it. Global and local superlinear/quadratic convergence results were obtained under mild conditions, and the finite termination property was also shown for the linear BVIs. Numerical results suggest that the method is efficient and promising.
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Communicated by Zhang Shi-sheng
Project supported by the Teaching and Research Award Program for the Outstanding Young Teachers in Higher Education Institutes of Munistry of Education, P. R. China
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Ulji, Guo-qing, C. New simple smooth merit function for box constrained variational inequalities and damped Newton type method. Appl Math Mech 26, 1083–1092 (2005). https://doi.org/10.1007/BF02466422
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DOI: https://doi.org/10.1007/BF02466422
Key words
- box constrained variational inequalities
- global convergence
- local superlinear or quadratic convergence
- finite termination property