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The length of the primal-dual path in Moreau-Yosida-based path-following methods for state constrained optimal control
Publikationstyp
Journal Article
Date Issued
2014
Sprache
English
Institut
TORE-URI
Journal
Volume
24
Issue
1
Start Page
108
End Page
126
Citation
SIAM Journal on Optimization 24 (1): 108-126 (2014)
Publisher DOI
Scopus ID
Publisher
SIAM
A priori estimates of the length of the primal-dual path resulting from a Moreau- Yosida approximation of the feasible set for state constrained optimal control problems are derived. These bounds depend on the regularity of the state and the dimension of the problem. Numerical results indicate that the bounds are indeed sharp and are typically attained in cases where the active set consists of isolated active points. Further conditions on the multiplier approximation are identified which guarantee higher convergence rates for the feasibility violation due to the Moreau-Yosida approximation process. Numerical experiments show again that the results are sharp and accurately predict the convergence behavior. © 2014 Society for Industrial and Applied Mathematics.
Subjects
Moreau-Yosida regularization
Path-following
PDE constrained optimization
Pointwise state constraints
Regularization error
DDC Class
510: Mathematik