Direct Multiple Shooting for Parabolic PDE Constrained Optimization

DOI10.1007/978-3-319-23321-5_6zbMath1337.65054OpenAlexW2506611779MaRDI QIDQ2801809

Andreas Potschka

Publication date: 22 April 2016

Published in: Contributions in Mathematical and Computational Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-23321-5_6

zbMATH Keywords

optimal controlquadratic programmingchemotaxisparabolic equationadvection-diffusionnumerical resultmultiple shootingNewton-Picard preconditioning

Mathematics Subject Classification ID

Taxonomy, cladistics, statistics in mathematical biology (92B10) Numerical optimization and variational techniques (65K10) Newton-type methods (49M15) Numerical methods based on nonlinear programming (49M37) Existence theories for optimal control problems involving partial differential equations (49J20) Preconditioners for iterative methods (65F08)

Related Items (5)

A parallel-in-time multiple shooting algorithm for large-scale PDE-constrained optimal control problems ⋮ Newton--Picard Preconditioners for Time-Periodic Parabolic Optimal Control Problems ⋮ An SQP-based multiple shooting algorithm for large-scale PDE-constrained optimal control problems ⋮ Parallel-in-time multiple shooting for optimal control problems governed by the Navier-Stokes equations ⋮ A sequential homotopy method for mathematical programming problems

Uses Software

• NewtonLib
• MUSCOP
• DAESOL-II
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Cites Work

• Model and analysis of chemotactic bacterial patterns in a liquid medium
• On shooting methods for boundary value problems
• A collocation method for boundary value problems
• Newton–Picard-Based Preconditioning for Linear-Quadratic Optimization Problems with Time-Periodic Parabolic PDE Constraints
• Optimization with PDE Constraints
• Evaluating Derivatives
• A minima tracking variant of semi-infinite programming for the treatment of path constraints within direct solution of optimal control problems
• Optimal control via collocation and non-linear programming
• An Adaptive Newton--Picard Algorithm with Subspace Iteration for Computing Periodic Solutions
• Optimale Steuerung partieller Differentialgleichungen
• Galerkin Finite Element Methods for Parabolic Problems
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