广义非线性集值混合拟变分包含的扰动近似点算法

本文研究一类广义非线性集值混合拟变分包含,概括了尚明生等人引入与研究过的熟知的广义集值变分包含类成特例.运用预解算子的技巧,建立了广义非线性集值混合拟变分包含与不动点问题之间的等价性,其中,预解算子JρA(·,x)是具有常数1/(1+cρ)的Lipschitz连续算子.本文还建立了几个扰动迭代算法,并提供了由算法生成的逼近解的收敛判据,所得算法与结果改进与推广了尚明生等人的相应算法与结果.

Perturbed Proximal Point Algorithm for Generalized Nonlinear Set-Valued Mixed Quasi-Variational Inclusions

The purpose of this paper is to study a class of generalized nonlinear set-valued mixed quasi-variational inclusions which includes the known class of generalized set-valued variational inclusions, introduced and studied by Shang et al., as a special case. Using the technique of resolvent operators, we establish the equivalence between the generalized nonlinear set-valued mixed quasi-variational inclusions and the fixed point problems, where the resolvent operatorsJpA(.,x) are Lipschitz continuous with constantl/(l cp), and also suggest some perturbed iterative algorithms. Further, we provide the convergence criteria for approximate solutions generated by the algorithms. The algorithms and results presented in this paper improve and generalize the corresponding algorithms and results of Shang et al.