NDLI: On state constraint representations and mesh-dependent gradient projection convergence rates for optimal control problems

Content Provider	IEEE Xplore Digital Library
Author	Dunn, J.C.
Copyright Year	2001
Description	Author affiliation: Dept. of Math., North Carolina State Univ., Raleigh, NC, USA (Dunn, J.C.)
Abstract	This note briefly summarizes the main results in a SIAM article (Dunn, 2000) with the same title. In the SIAM paper, two distinct nonlinear programming formulations are investigated for ODE optimal control problems with pointwise state and control constraints. The first formulation treats the differential equations of state as an equality constraint in the conventional manner. The second formulation employs a different equality constraint entailing the integrated state transition map. Related convergence rate estimates are developed for augmented gradient projection methods and discrete-time approximations to a large representative class of ODE control problems. In the first formulation, the rate estimates are mesh-dependent, and the predicted number of inner loop gradient projection iterations needed to achieve a fixed small deviation from the optimal value of the augmented Lagrangian is inversely proportional to the square of the mesh width. In the second formulation, the convergence rates and predicted iteration counts are mesh-invariant. The computational costs-per-iteration in the two formulations are comparable.
Sponsorship	IEEE Control Syst. Soc
Starting Page	3564
Ending Page	3568
File Size	367574
Page Count	5
File Format	PDF
ISBN	0780370619
DOI	10.1109/CDC.2001.980412
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2001-12-04
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Convergence Optimized production technology Optimal control Strain control Differential equations Lagrangian functions Iterative methods Iterative algorithms Mathematics Bibliographies
Content Type	Text
Resource Type	Article

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