The roughness of the model function f（x） to the basis functions has been identified. When the model function is continuous segment, its roughness does not depend on the behavior of the first segment, but depends on ...The roughness of the model function f（x） to the basis functions has been identified. When the model function is continuous segment, its roughness does not depend on the behavior of the first segment, but depends on ＂h＂, the shift in the slope of two consecutive segments. If the distribution of design is uniform, f（x） is continuous segment function, and h is constant, then the maximum roughness is h2/192 obtained at the midpoint of the observations. Suppose that we have a sequence of designs {Pn（x）} then its corresponding distribution {Fn （x）} converges weakly to some distribution F（x）. Let D（f） be a set of discontinuous points off（x）, it is possible to take the limit of the roughness if D（f） has zero （dF）-measure. The behavior of maximum roughness of the discontinuous segment function has been studied by using grid points.展开更多
This paper introduces and considers a new system of generalized mixed variational inequal- ities in a Hilbert space, which includes many new and known systems of variational inequalities and generalized variational in...This paper introduces and considers a new system of generalized mixed variational inequal- ities in a Hilbert space, which includes many new and known systems of variational inequalities and generalized variational inequalities as special cases. By using the two concepts of η-subdifferential and η-proximal mappings of a proper function, the authors try to demonstrate that the system of generalized mixed variational inequalities is equivalence with a fixed point problem. By applying the equivalence, a new and innovative η-proximal point algorithm for finding approximate solutions of the system of generalized mixed variational inequalities will be suggested and analyzed. The authors also study the convergence analysis of the new iterative method under much weaker conditions. The results can be viewed as a refinement and improvement of the previously known results for variational inequalities.展开更多
文摘The roughness of the model function f（x） to the basis functions has been identified. When the model function is continuous segment, its roughness does not depend on the behavior of the first segment, but depends on ＂h＂, the shift in the slope of two consecutive segments. If the distribution of design is uniform, f（x） is continuous segment function, and h is constant, then the maximum roughness is h2/192 obtained at the midpoint of the observations. Suppose that we have a sequence of designs {Pn（x）} then its corresponding distribution {Fn （x）} converges weakly to some distribution F（x）. Let D（f） be a set of discontinuous points off（x）, it is possible to take the limit of the roughness if D（f） has zero （dF）-measure. The behavior of maximum roughness of the discontinuous segment function has been studied by using grid points.
基金supported by the Natural Science Foundation of China under Grant No.11001287the Natural Science Foundation Project of CSTC under Grant No.2010BB9254
文摘This paper introduces and considers a new system of generalized mixed variational inequal- ities in a Hilbert space, which includes many new and known systems of variational inequalities and generalized variational inequalities as special cases. By using the two concepts of η-subdifferential and η-proximal mappings of a proper function, the authors try to demonstrate that the system of generalized mixed variational inequalities is equivalence with a fixed point problem. By applying the equivalence, a new and innovative η-proximal point algorithm for finding approximate solutions of the system of generalized mixed variational inequalities will be suggested and analyzed. The authors also study the convergence analysis of the new iterative method under much weaker conditions. The results can be viewed as a refinement and improvement of the previously known results for variational inequalities.
