A Regularized Variational Inequality Approach for Nonlinear Monotone Ill-Posed Equations

被引：1

作者：

Plato, Robert ^{[1
]}

Hofmann, Bernd ^{[2
]}

机构：

[1] Univ Siegen, Dept Math, Walter Flex Str 3, D-57068 Siegen, Germany

[2] Tech Univ Chemnitz, Fac Math, D-09107 Chemnitz, Germany

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2019年 / 182卷 / 02期

关键词：

Nonlinear ill-posed problem; Monotone operator; Variational inequality; Lavrentiev regularization; Adjoint source condition; A priori parameter choice; OPERATORS; CONVERGENCE;

D O I：

10.1007/s10957-019-01531-w

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

We consider a regularized variational inequality approach for the stable solution of nonlinear ill-posed problems, where the involved operators are monotone on a given closed, convex subset of a Hilbert space. For suitable a priori parameter choices, we present new error estimates for the subclass of cocoercive operators, provided that the solution admits an adjoint source representation. Some numerical experiments are included.

引用

页码：525 / 539

页数：15

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