Local convergence of the steepest descent method in Hilbert spaces

DOI10.1016/j.jmaa.2004.06.051zbMath1062.65060OpenAlexW2028091727MaRDI QIDQ703669

D. Kharzeev

Publication date: 11 January 2005

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2004.06.051

zbMATH Keywords

convergencePalais-Smale conditionHilbert spacesteepest descent methodlocally Lipschitz continuous operatorPicard-Lindelöf theoremSobolev embeding theorem

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (7)

A numerical damped oscillator approach to constrained Schrödinger equations ⋮ Learning-informed parameter identification in nonlinear time-dependent PDEs ⋮ A gradient-descent method for curve fitting on Riemannian manifolds ⋮ Unnamed Item ⋮ Nonsmooth steepest descent method by proximal subdifferentials in Hilbert spaces ⋮ Optimal Energy Shaping via Neural Approximators ⋮ Dynamical representations of constrained multicomponent nonlinear Schrödinger equations in arbitrary dimensions

Cites Work

• Some effective methods for unconstrained optimization based on the solution of systems of ordinary differential equations
• Differential gradient methods
• Ordinary differential equations. An introduction to nonlinear analysis. Transl. from the German by Gerhard Metzen
• An Algorithm, Based on Singular Perturbation Theory, for Ill-Conditioned Minimization Problems
• A new arc algorithm for unconstrained optimization
• Gradient method for non-injective operators in Hilbert space with application to Neumann problems
• Recent advances in unconstrained optimization
• On the gradient method in a Hilbert space in the case of nonisolated minima
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