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

MSC:

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)
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[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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