Abstract

A brief survey is given concerning iterative processes of Fejér type for basic statements of ill-posed problems, including constrained quadratic and convex minimization problems, variational inequalities, and linear and nonlinear operator equations in Hilbert spaces. By applying the method of successive approximations and its modification using correction factors, all these statements reduce to the problem of finding fixed points of nonexpansive Fejér operators. Material is also presented related to a two-stage method of constructing a regularizing algorithm for nonlinear ill-posed problems with monotone operators. An economic way is described by which the algorithm takes into account additional a priori information on the solution using Fejér maps.

中文翻译：

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不适定问题中的迭代Fejér过程

摘要

对于Fejér类型的迭代过程，针对不适定问题的基本陈述进行了简短的调查，这些问题包括Hilbert空间中受约束的二次和凸极小化问题，变分不等式以及线性和非线性算子方程。通过应用逐次逼近法及其使用校正因子的修改，所有这些陈述都减少了寻找非扩张Fejér算子的不动点的问题。还介绍了与使用单调算子构造非线性不适定问题的正则化算法的两阶段方法有关的材料。描述了一种经济的方法，通过该方法，算法可以使用Fejér映射考虑解决方案上的其他先验信息。