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Partitioned variable metric updates for large structured optimization problems. (English) Zbl 0482.65035

65K05 Numerical mathematical programming methods
90C20 Quadratic programming
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[1] Axelsson, O.: Solution of linear systems of equations: Iterative Methods. In: Sparse matrix techniques. V.A. Baker ed. Copenhagen 1976. Springer Verlag Berlin 1976 · Zbl 0334.65028
[2] Brandt, A.: Multi-level adaptative solutions to boundary value problems. Math. Comput.31, 333-390 (1977) · Zbl 0373.65054
[3] Davidon, W.C.: Variable metric method for minimization. Technical Report #ANL-5990 (Rev.), Argonne National Laboratory, Research and Development 1959 · Zbl 0752.90062
[4] Dennis, J.E., Moré, J.J.: Quasi-Newton methods: Motivation and theory. SIAM Rev.19, 46-89 (1977) · Zbl 0356.65041
[5] Dixon, L.C.W.: The solution of the Navier-Stokes equations via finite elements and optimization on a parallel processor. Presented at the CEC/CREST International Summer School on Numerical Algorithms for Parallel Processors. Bergamo, Italy June 1981
[6] Ekeland, I., Temam, R.: Convex analysis and variational problems. North-Holland: Amsterdam 1976 · Zbl 0322.90046
[7] Fletcher, R., Powell, M.J.D.: On the modification ofLDL 1 factorisations. Math. Comput.28, 1067-1087 (1974) · Zbl 0293.65018
[8] Gill, P., Murray, W.: Conjugate gradient methods for large scale nonlinear optimization. Technical Report SOL 79-15, Department of Operations Research, Stanford University, Stanford 1979
[9] Greenstadt, J.: Variations upon variable metric methods. Math. Comput.24, 1-18 (1970) · Zbl 0204.49601
[10] Griewank, A., Toint, Ph.L.: On the unconstrained optimization of partially separable functions. In: Nonlinear optimization, M.J.D. Powell ed. Academic Press: New York (1981) · Zbl 0563.90085
[11] Gustafsson, I.: Stability and rate of convergence of modified incomplete factorisation methods. Research Report 79.02 R Department of Computer Science, University of Göteborg (1979) · Zbl 0417.65052
[12] Huang, H.Y.: Unified Approach to quadratically convergent algorithms for function minimization. J. Optimization Theory Appl.5, 405-423 (1970) · Zbl 0194.19402
[13] Kamat, M.P., Vanden Brink, D.J., Watson, L.T.: Non-linear structural analysis using quasi-Newton minimization algorithms that exploit sparsity. Presented at the International Conference on Numerical Methods for Nonlinear Problems, Swansea, U.K. (1980)
[14] Marwil, E.: Exploiting sparsity in Newton-like methods. PhD thesis, Cornell University, Ithaca, New York (1978)
[15] Oren, S.S., Spedicato, E.: Optimal conditioning of self-scaling variable metric algorithms. Math. Programming10, 70-90 (1976) · Zbl 0342.90045
[16] Powell, M.J.D.: Restart procedures for the conjugate gradient method. Math. Programming12, 241-254 (1977) · Zbl 0396.90072
[17] Powell, M.J.D.: Some global convergence properties of a variable metric algorithm for minimization without exact line searches. SIAM-AMS Proceedings9, 53-72 (1976) · Zbl 0338.65038
[18] Shanno, D.F.: On variable metric methods for sparse hessians. Math. Comput.34, 499-514 (1980) · Zbl 0424.65027
[19] Shanno, D.F., Phua, K.H.: Matrix conditionning and nonlinear optimization. Math. Programming14 (1978) · Zbl 0371.90109
[20] Stetter, H.J.: Analysis of discretization methods for ordinary differential equations. Springer tracts on Natural Philosophy23 (1973) · Zbl 0276.65001
[21] Toint, Ph.L.: On sparse and symmetric matrix updating subject to a linear equation. Math. Comput.31, 954-961 (1977) · Zbl 0379.65034
[22] Toint, Ph.L.: A note on sparsity exploiting quasi-Newton methods. Math. Programming21, 172-181 (1981) · Zbl 0463.90081
[23] Toint, Ph.L.: Towards an efficient sparsity exploiting Newton method. In: Sparse matrices and their uses. I.S. Duff ed. Academic Press: New York 1981 · Zbl 0463.90081
[24] Toint, Ph.L., Strodiot, J.J.: An algorithm for unconstrained minimization of large scale problems by Decomposition in subspaces. Technical Report 76/1. Department of Maths, FUN Namur, Belgium 1976
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