Parametric continuation method with correction and its applications

DOI10.1007/s10598-009-9037-yzbMath1181.65097OpenAlexW2161994909MaRDI QIDQ1037063

S. S. Zhulin

Publication date: 13 November 2009

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

Full work available at URL: https://doi.org/10.1007/s10598-009-9037-y

zbMATH Keywords

algorithmboundary-value problemnonlinear equationsoptimal control problemPontryagin maximum principlehomotopy theoryparametric continuation methodNewton homotopyfixed point homotopyPontryagin extremal solution

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Newton-type methods (49M15) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Existence theories for optimal control problems involving ordinary differential equations (49J15)

Cites Work

• Continuation by parameter scheme in nonlinear boundary-value problem of maximum principle
• Approximate quasi-Newton methods
• Continuation in shooting methods for two-point boundary value problems
• Convergence behaviour of inexact Newton methods
• The inexact, inexact perturbed, and quasi-Newton methods are equivalent models
• A parameter extension method for solving boundary value problems in optimal control theory
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