Large-scale optimization with linear equality constraints using reduced compact representation. (English) Zbl 07459362


68Q25 Analysis of algorithms and problem complexity
68R10 Graph theory (including graph drawing) in computer science
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
Full Text: DOI arXiv


[1] S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, Distributed optimization and statistical learning via the alternating direction method of multipliers, Found. Trends Mach. Learn., 3 (2011), pp. 1-122, https://doi.org/10.1561/2200000016. · Zbl 1229.90122
[2] C. G. Broyden, The convergence of a class of double-rank minimization algorithms 1. General considerations, IMA J. Appl. Math., 6 (1970), pp. 76-90, https://doi.org/10.1093/imamat/6.1.76. · Zbl 0223.65023
[3] J. Brust, O. Burdakov, J. Erway, and R. Marcia, A dense initialization for limited-memory quasi-Newton methods, Comput. Optim. Appl., 74 (2019), pp. 121-142. · Zbl 1427.90292
[4] J. J. Brust, Large-Scale Quasi-Newton Trust-Region Methods: High-Accuracy Solvers, Dense Initializations, and Extensions, PhD thesis, University of California, Merced, 2018, https://escholarship.org/uc/item/2bv922qk.
[5] J. J. Brust, J. B. Erway, and R. F. Marcia, On solving L-SR1 trust-region subproblems, Comput. Optim. Appl., 66 (2017), pp. 245-266. · Zbl 1364.90239
[6] J. J. Brust, R. F. Marcia, and C. G. Petra, Large-scale quasi-Newton trust-region methods with low-dimensional linear equality constraints, Comput. Optim. Appl., 74 (2019), pp. 669-701, https://doi.org/10.1007/s10589-019-00127-4. · Zbl 1435.90147
[7] O. Burdakov, L. Gong, Y.-X. Yuan, and S. Zikrin, On efficiently combining limited memory and trust-region techniques, Math. Program. Comput., 9 (2016), pp. 101-134. · Zbl 1368.90103
[8] R. H. Byrd, J. Nocedal, and R. B. Schnabel, Representations of quasi-Newton matrices and their use in limited-memory methods, Math. Program., 63 (1994), pp. 129-156. · Zbl 0809.90116
[9] R. H. Byrd, J. Nocedal, and R. A. Waltz, Knitro: An Integrated Package for Nonlinear Optimization, Springer US, Boston, MA, 2006, pp. 35-59, https://doi.org/10.1007/0-387-30065-1_4. · Zbl 1108.90004
[10] A. R. Conn, N. I. M. Gould, and P. L. Toint, Trust-Region Methods, SIAM, Philadelphia, PA, 2000. · Zbl 0958.65071
[11] T. A. Davis, Algorithm 915, SuiteSparseQR: Multifrontal multithreaded rank-revealing sparse QR factorization, ACM Trans. Math. Software, 38 (2011), pp. 8:1-22. · Zbl 1365.65122
[12] T. A. Davis and Y. Hu, The University of Florida sparse matrix collection, ACM Trans. Math. Software, 38 (2011), p. 25. · Zbl 1365.65123
[13] T. A. Davis, Y. Hu, and S. Kolodziej, SuiteSparse Matrix Collection, https://sparse.tamu.edu/, 2015-present.
[14] O. DeGuchy, J. B. Erway, and R. F. Marcia, Compact representation of the full Broyden class of quasi-Newton updates, Numer. Linear Algebra Appl., 25 (2018), e2186. · Zbl 06987009
[15] E. Dolan and J. Moré, Benchmarking optimization software with performance profiles, Math. Program., 91 (2002), pp. 201-213. · Zbl 1049.90004
[16] R. Fletcher, A new approach to variable metric algorithms, Comput. J., 13 (1970), pp. 317-322, https://doi.org/10.1093/comjnl/13.3.317. · Zbl 0207.17402
[17] D. C.-L. Fong and M. Saunders, LSMR: An iterative algorithm for least-squares problems, SIAM J. Sci. Comput., 33 (2011), pp. 2950-2971, https://doi.org/10.1137/10079687X. · Zbl 1232.65052
[18] A. Fu, J. Zhang, and S. Boyd, Anderson accelerated Douglas-Rachford splitting, SIAM J. Sci. Comput., 42 (2020), pp. A3560-A3583, https://doi.org/10.1137/19M1290097. · Zbl 1458.90511
[19] P. E. Gill and W. Murray, Numerical Methods for Constrained Optimization, Academic Press, London, 1974. · Zbl 0297.90082
[20] D. Goldfarb, A family of variable-metric methods derived by variational means, Math. Comp., 24 (1970), pp. 23-26, https://doi.org/10.1090/S0025-5718-1970-0258249-6. · Zbl 0196.18002
[21] G. H. Golub and C. F. Van Loan, Matrix Computations, 4th ed., Johns Hopkins Stud. Math. Sci., Johns Hopkins University Press, Baltimore, MD, 2013. · Zbl 1268.65037
[22] N. I. M. Gould, D. Orban, and P. L. Toint, CUTEr and SifDec: A constrained and unconstrained testing environment, revisited, ACM Trans. Math. Software, 29 (2003), pp. 373-394. · Zbl 1068.90526
[23] M. R. Hestenes and E. Stiefel, Methods of conjugate gradients for solving linear systems, J. Res. Natl. Bureau. Standards, 49 (1952), pp. 409-436. · Zbl 0048.09901
[24] D. C. Liu and J. Nocedal, On the limited memory BFGS method for large scale optimization, Math. Program., 45 (1989), pp. 503-528. · Zbl 0696.90048
[25] A. Mahajan, S. Leyffer, and C. Kirches, Solving Mixed-Integer Nonlinear Programs by QP Diving, Technical Report ANL/MCS-P2071-0312, Mathematics and Computer Science Division, Argonne National Laboratory, Lemont, IL, 2012.
[26] J. Nocedal, Updating quasi-Newton matrices with limited storage, Math. Comp., 35 (1980), pp. 773-782. · Zbl 0464.65037
[27] J. Nocedal and S. J. Wright, Numerical Optimization, 2nd ed., Springer-Verlag, New York, 2006. · Zbl 1104.65059
[28] C. C. Paige and M. A. Saunders, LSQR: An algorithm for sparse linear equations and sparse least squares, ACM Trans. Math. Software, 8 (1982a), pp. 43-71, https://doi.org/10.1145/355984.355989. · Zbl 0478.65016
[29] D. F. Shanno, Conditioning of quasi-Newton methods for function minimization, Math. Comp., 24 (1970), pp. 647-656, https://doi.org/10.1090/S0025-5718-1970-0274029-X. · Zbl 0225.65073
[30] A. Wächter and L. T. Biegler, On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming, Math. Program., 106 (2006), pp. 25-57. · Zbl 1134.90542
[31] H. Zhang and W. W. Hager, A nonmonotone line search technique and its application to unconstrained optimization, SIAM J. Optim., 14 (2004), pp. 1043-1056, https://doi.org/10.1137/S1052623403428208. · Zbl 1073.90024
[32] C. Zhu, R. H. Byrd, P. Lu, and J. Nocedal, Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization, ACM Trans. Math. Software, 23 (1997), pp. 550-560, https://doi.org/10.1145/279232.279236. · Zbl 0912.65057
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