State-defect constraint pairing graph coarsening method for Karush–Kuhn–Tucker matrices arising in orthogonal collocation methods for optimal control

Begüm Şenses Cannataro (), Anil V. Rao () and Timothy A. Davis ()
Additional contact information
Begüm Şenses Cannataro: University of Florida
Anil V. Rao: University of Florida
Timothy A. Davis: Texas A&M University

Computational Optimization and Applications, 2016, vol. 64, issue 3, No 7, 793-819

Abstract: Abstract A state-defect constraint pairing graph coarsening method is described for improving computational efficiency during the numerical factorization of large sparse Karush–Kuhn–Tucker matrices that arise from the discretization of optimal control problems via an Legendre–Gauss–Radau orthogonal collocation method. The method takes advantage of the particular sparse structure of the Karush–Kuhn–Tucker matrix that arises from the orthogonal collocation method. The state-defect constraint pairing graph coarsening method pairs each component of the state with its corresponding defect constraint and forces paired rows to be adjacent in the reordered Karush–Kuhn–Tucker matrix. Aggregate state-defect constraint pairing results are presented using a wide variety of benchmark optimal control problems where it is found that the proposed state-defect constraint pairing graph coarsening method significantly reduces both the number of delayed pivots and the number of floating point operations and increases the computational efficiency by performing more floating point operations per unit time. It is then shown that the state-defect constraint pairing graph coarsening method is less effective on Karush–Kuhn–Tucker matrices arising from Legendre–Gauss–Radau collocation when the optimal control problem contains state and control equality path constraints because such matrices may have delayed pivots that correspond to both defect and path constraints. An alternate graph coarsening method that employs maximal matching is then used to attempt to further reduce the number of delayed pivots. It is found, however, that this alternate graph coarsening method provides no further advantage over the state-defect constraint pairing graph coarsening method.

Keywords: Karush–Kuhn–Tucker systems; Graph coarsening; Optimal control; Orthogonal collocation methods (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10589-015-9821-x Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:64:y:2016:i:3:d:10.1007_s10589-015-9821-x

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-015-9821-x

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().