An MP-Newton method for computing nonlinear eigenpairs and its application for solving a semilinear Schrödinger equation

DOI10.1016/j.cam.2024.116315MaRDI QIDQ6653568

Xudong Yao

Publication date: 16 December 2024

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

zbMATH Keywords

convergenceLagrange multiplier functionMP-Newton methodnonlinear eigenpairorthogonal-max type critical point

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Newton-type methods (49M15) Fréchet and Gateaux differentiability in optimization (49J50) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05)

Cites Work

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• A quasi-local Gross-Pitaevskii equation for attractive Bose-Einstein condensates
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• Optimizing Schrödinger Functionals Using Sobolev Gradients: Applications to Quantum Mechanics and Nonlinear Optics
• Numerical Methods for Computing Nonlinear Eigenpairs: Part II. Non-Iso-Homogeneous Cases
• A high-linking algorithm for sign-changing solutions of semilinear elliptic equations
• Computing the Ground State Solution of Bose--Einstein Condensates by a Normalized Gradient Flow
• A mountain pass method for the numerical solution of semilinear elliptic problems

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