SMOOTHING TECHNIQUE OF NONSMOOTH NEWTON METHODS FOR CONTROL-STATE CONSTRAINED OPTIMAL CONTROL PROBLEMS

This paper is concerned with the numerical solution of optimal control problems subject to mixed control-state constraints with differential-algebraic equations. The necessary conditions arising from a local minimum principle are transformed into an equivalent nonsmooth equation in appropriate Banac...

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Published inSIAM journal on numerical analysis Vol. 50; no. 4; pp. 1982 - 2011
Main Authors CHEN, JINHAI, GERDTS, MATTHIAS
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2012
Subjects
Adjoints
Algebra
Banach space
Banach spaces
Convergence
Data smoothing
Equivalence
Globalization
Mathematical analysis
Mathematical complements
Mathematical inequalities
Mathematics
Methods
Newton methods
Newtons method
Numerical analysis
Optimal control
Optimization and Control
Smoothing
Variational inequalities
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ISSN0036-1429
1095-7170
DOI10.1137/110822177

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Summary:This paper is concerned with the numerical solution of optimal control problems subject to mixed control-state constraints with differential-algebraic equations. The necessary conditions arising from a local minimum principle are transformed into an equivalent nonsmooth equation in appropriate Banach spaces. We then develop a parametric smoothing Newton method for solving this nonsmooth equation. The global and local convergence is proposed under suitable settings. Numerical examples are presented to demonstrate the efficiency of our global smoothing technique.
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ISSN:0036-1429
1095-7170
DOI:10.1137/110822177