非凸泛函下的完全广义拟变分类包含关系
Completely Generalized Quasi-Variational-Like Inclusions with Nonconvex Functionals
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摘要: 引进了Hilbert空间中真泛函的两个新概念:η-次微分和η-逼近映射,并且指出了η-逼近映射的存在性和连续性.利用这两个新的概念,研究了在非凸泛函下的一类完全广义拟变分类包含关系,给出了一种寻找近似解的新的迭代算法,并且也证明了由这种迭代算法所产生的迭代序列的收敛性.Abstract: In this paper, two new concepts of η-subdifferential and η-proximal mappings of proper functionals are introduced in Hilbert spaces, and the existence and Lipschitz continuity of the η-proximal mapping are shown. By applying these concepts, a class of completely generalized quasi-variational-like inclusions with a nonconvex functionals are introduced and studied. A new iterative algorithms for finding the approximate solutions and the convergence criteria of the iterative sequences generated by the algorithms are also given.
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