Globally strongly convex cost functional for a coefficient inverse problem

被引：37

作者：

Beilina, Larisa ^{[1
,2
]}

Klibanov, Michael V. ^{[3
]}

机构：

[1] Chalmers Univ Technol, Dept Math Sci, SE-42196 Gothenburg, Sweden

[2] Gothenburg Univ, Dept Math Sci, SE-42196 Gothenburg, Sweden

[3] Univ N Carolina, Dept Math & Stat, Charlotte, NC 28223 USA

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2015年 / 22卷

基金：

瑞典研究理事会;

关键词：

Coefficient inverse problem; Wave-like equation; Carleman weight function; Strongly convex cost functional;

D O I：

10.1016/j.nonrwa.2014.09.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A Carleman Weight Function (CWF) is used to construct a new cost functional for a Coefficient Inverse Problems for a hyperbolic PDE. Given a bounded set of an arbitrary size in a certain Sobolev space, one can choose the parameter of the CWF in such a way that the constructed cost functional will be strongly convex on that set. Next, convergence of the gradient method, which starts from an arbitrary point of that set, is established. Since restrictions on the size of that set are not imposed, then this is the global convergence. (C) 2014 Elsevier Ltd. All rights reserved.

引用

页码：272 / 288

页数：17

共 20 条

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[2]

[Anonymous], 1971, EQUATIONS MATH PHYS

[3]

[Anonymous], 2004, INVER ILL POSED PROB, DOI 10.1515/9783110915549

[4] Approximation of unbounded operators by bounded operators and related extremal problems [J].