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, Volume 63, Issue 1, pp 129156
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Representations of quasiNewton matrices and their use in limited memory methods
 Richard H. ByrdAffiliated withComputer Science Department, University of Colorado
 , Jorge NocedalAffiliated withDepartment of Electrical Engineering and Computer Science, Northwestern University
 , Robert B. SchnabelAffiliated withComputer Science Department, University of Colorado
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We derive compact representations of BFGS and symmetric rankone matrices for optimization. These representations allow us to efficiently implement limited memory methods for large constrained optimization problems. In particular, we discuss how to compute projections of limited memory matrices onto subspaces. We also present a compact representation of the matrices generated by Broyden's update for solving systems of nonlinear equations.
Key words
QuasiNewton method constrained optimization limited memory method largescale optimization Title
 Representations of quasiNewton matrices and their use in limited memory methods
 Journal

Mathematical Programming
Volume 63, Issue 13 , pp 129156
 Cover Date
 199401
 DOI
 10.1007/BF01582063
 Print ISSN
 00255610
 Online ISSN
 14364646
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 QuasiNewton method
 constrained optimization
 limited memory method
 largescale optimization
 Industry Sectors
 Authors

 Richard H. Byrd ^{(1)}
 Jorge Nocedal ^{(2)}
 Robert B. Schnabel ^{(1)}
 Author Affiliations

 1. Computer Science Department, University of Colorado, Boulder, CO, USA
 2. Department of Electrical Engineering and Computer Science, Northwestern University, 602083118, Evanston, IL, USA