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Title: Large-Scale Optimization with Linear Equality Constraints Using Reduced Compact Representation

Journal Article · · SIAM Journal on Scientific Computing
DOI: https://doi.org/10.1137/21m1393819 · OSTI ID:1869517
 [1]; ORCiD logo [2]; ORCiD logo [3]; ORCiD logo [4]
  1. Univ. of California, San Diego, CA (United States)
  2. Univ. of California, Merced, CA (United States)
  3. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
  4. Stanford Univ., CA (United States)
+ Show Author Affiliations

For optimization problems with linear equality constraints, we prove that the (1,1) block of the inverse KKT matrix remains unchanged when projected onto the nullspace of the constraint matrix. In this work, we develop reduced compact representations of the limited-memory inverse BFGS Hessian to compute search directions efficiently when the constraint Jacobian is sparse. Orthogonal projections are implemented by a sparse QR factorization or a preconditioned LSQR iteration. In numerical experiments two proposed trust-region algorithms improve in computation times, often significantly, compared to previous implementations of related algorithms and compared to IPOPT.

Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF)
Grant/Contract Number:
AC52-07NA27344; AC02-06CH11357
OSTI ID:
1869517
Report Number(s):
LLNL-JRNL-818401; 1029019
Journal Information:
SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 1 Vol. 44; ISSN 1064-8275
Publisher:
Society for Industrial and Applied Mathematics (SIAM)Copyright Statement
Country of Publication:
United States
Language:
English

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Related Subjects

97 MATHEMATICS AND COMPUTING
LSQR
compact representation
large-scale optimization
limited memory
sparse QR
trust-region method