Globally strongly convex cost functional for a coefficient inverse problem

2013/12/10 by Larisa Beilina, Beilina, Larisa, Michael V. Klibanov +1
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Analytic and geometric function theory #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Optimization and Variational Analysis #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1312.2886

arxiv created 2013/12/10 · openalex publication_date 2013/12/10 · arxiv updated 2013/12/11 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

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.

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