Quasi-convex sets and size \(\times\) curvature condition, application to nonlinear inversion

DOI10.1007/BF01447739zbMath0779.47043MaRDI QIDQ1179160

Guy Chavent

Publication date: 26 June 1992

Published in: Applied Mathematics and Optimization (Search for Journal in Brave)

zbMATH Keywords

parameter estimationinverse problemslocal minimaapproximation theorynonlinear least squaresnonlinear operatorsprojection theoryquasi-convex setscylindrical neighborhoodwellposedness of nonlinear least square problems

Mathematics Subject Classification ID

Existence theories for problems in abstract spaces (49J27) Nonlinear operators and their properties (47H99)

Related Items (4)

A geometric theory for \(L^ 2\)-stability of the inverse problem in a one-dimensional elliptic equation from an \(H^ 1\)-observation ⋮ A survey of recent[1985-1995advances in generalized convexity with applications to duality theory and optimality conditions] ⋮ The Output Least Squares Identifiability of the Diffusion Coefficient from an H¹–Observation in a 2–D Elliptic Equation ⋮ Criteria for global minimum of sum of squares in nonlinear regression

Cites Work

• The Lipschitz continuity of the metric projection
• Output least squares stability in elliptic systems
• Unique best approximation from a \(C^2\)-manifold in Hilbert space
• Stability for parameter estimation in two point boundary value problems.
• On the uniqueness of local minima for general abstract nonlinear least-squares problems
• Global inversion theorems and applications to differential equations
• The plane-wave detection problem
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