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Damped Dynamical Systems for Solving Equations and Optimization Problems
Örebro University, School of Science and Technology.ORCID iD: 0000-0003-0332-2315
Örebro University, School of Science and Technology.ORCID iD: 0000-0002-2630-7479
Department of Mathematics, University of Bergen, Norway.
Faculty of Mathematics, Chemnitz University of Technology, Germany.ORCID iD: 0000-0003-4023-6352
2019 (English)In: Handbook of the Mathematics of the Arts and Sciences / [ed] Bharath Sriraman, Springer , 2019Chapter in book (Other academic)
Abstract [en]

We present an approach for solving optimization problems with or without constrains which we call Dynamical Functional Particle Method (DFMP). The method consists of formulating the optimization problem as a second order damped dynamical system and then applying symplectic method to solve it numerically. In the first part of the chapter, we give an overview of the method and provide necessary mathematical background. We show that DFPM is a stable, efficient, and given the optimal choice of parameters, competitive method. Optimal parameters are derived for linear systems of equations, linear least squares, and linear eigenvalue problems. A framework for solving nonlinear problems is developed and numerically tested. In the second part, we adopt the method to several important applications such as image analysis, inverse problems for partial differential equations, and quantum physics.  At the end, we present open problems and share some ideas of future work on generalized (nonlinear) eigenvalue problems, handling constraints with reflection, global optimization, and nonlinear ill-posed problems.

Place, publisher, year, edition, pages
Springer , 2019.
Keywords [en]
Optimization, damped dynamical systems, convex problems, eigenvalue problems, image analysis, inverse problems, quantum physics, Schrödinger equation
National Category
Computational Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:oru:diva-71881DOI: 10.1007/978-3-319-70658-0ISBN: 978-3-319-70658-0 (electronic)OAI: oai:DiVA.org:oru-71881DiVA, id: diva2:1283319
Available from: 2019-01-29 Created: 2019-01-29 Last updated: 2019-04-01Bibliographically approved

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Gulliksson, MårtenÖgren, MagnusZhang, Ye

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
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  • de-DE
  • en-GB
  • en-US
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  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
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