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Large-scale linearly constrained optimization. (English) Zbl 0383.90074

MSC:
90C06 Large-scale problems in mathematical programming
65K05 Numerical mathematical programming methods
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[1] J. Abadie, ”Application of the GRG algorithm to optimal control problems”, in: J. Abadie, ed.,Integer and nonlinear programming (North-Holland, Amsterdam, 1970) pp. 191–211. · Zbl 0332.90040
[2] R.H. Bartels, ”A stabilization of the simplex method”,Numerische Mathematik 16 (1971) 414–434. · Zbl 0197.43305 · doi:10.1007/BF02169151
[3] R.H. Bartels and G.H. Golub, ”The simplex method of linear programming using LU decomposition”,Communications of ACM 12 (1969) 266–268. · Zbl 0181.19104 · doi:10.1145/362946.362974
[4] E.M.L. Beale, ”Numerical methods”, in: J. Abadie, ed.,Nonlinear programming (North-Holland, Amsterdam, 1967) pp. 132–205. · Zbl 0168.40602
[5] J. Bracken and G.P. McCormick,Selected applications of nonlinear programming (Wiley, New York, 1968).
[6] R.P. Brent, ”Reducing the retrieval time of scatter storage techniques”,Communications of ACM 16 (1973) 105–109. · Zbl 0251.68019 · doi:10.1145/361952.361964
[7] C.G. Broyden, ”Quasi-Newton methods”, in: W. Murray, ed.,Numerical methods for unconstrained optimization (Academic Press, New York, 1972) pp. 87–106.
[8] A. Buckley, ”An alternate implementation of Goldfarb’s minimization algorithm”,Mathematical Programming 8 (1975) 207–231. · Zbl 0309.90047 · doi:10.1007/BF01580443
[9] A.R. Colville, ”A comparative study on nonlinear programming codes”, IBM New York Scientific Center Report 320-2949 (1968).
[10] A.R. Conn, ”Linear programming via a non-differentiable penalty function”,SIAM Journal of Numerical Analysis 13 (1) (1976) 145–154. · Zbl 0333.90029 · doi:10.1137/0713016
[11] R.W. Cottle, ”The principal pivoting method of quadratic programming”, in: G.B. Dantzig and A.F. Veinott, Jr., eds.,Mathematics of the decision sciences, Part 1 (American Mathematical Society, 1968) pp. 144–162. · Zbl 0196.22902
[12] G.B. Dantzig,Linear programming and extensions (Princeton University Press, NJ, 1963).
[13] W.C. Davidon, ”Variable metric method for minimization”, AEC Research and Development Report ANL-5990 (1959). · Zbl 0752.90062
[14] I.S. Duff, ”On algorithms for obtaining a maximum transversal”, to appear.
[15] I.S. Duff and J.K. Reid, ”An implementation of Tarjan’s algorithm for the block triangularization of a matrix”, AERE Report C.S.S. 29 (1976), Harwell, England. · Zbl 0389.65019
[16] P. Faure and P. Huard, ”Resolution de programmes mathematiques a fonction nonlineaire par la methode du gradient reduit”,Revue Francaise de Recherche Operationelle 36 (1965) 167–206.
[17] R. Fletcher, ”Minimizing general functions subject to linear constraints”, in: F.A. Lootsma, ed.,Numerical methods for nonlinear optimization (Academic Press, London and New York, 1972) pp. 279–296.
[18] R. Fletcher and M.J.D. Powell, ”A rapidly convergent descent method for minimization”,Computer Journal 6 (1963) 163–168. · Zbl 0132.11603
[19] R. Fletcher and C.M. Reeves, ”Function minimization by conjugate gradients”,Computer Journal 7 (1964) 149–154. · Zbl 0132.11701 · doi:10.1093/comjnl/7.2.149
[20] P.E. Gill, G.H. Golub, W. Murray and M.A. Saunders, ”Methods for modifying matrix factorizations”,Mathematics of Computation 28 (1974) 505–535. · Zbl 0289.65021 · doi:10.1090/S0025-5718-1974-0343558-6
[21] P.E. Gill and W. Murray, ”Quasi-Newton methods for unconstrained optimization”,Journal of Institute of Mathematics and its Applications 9 (1972) 91–108. · Zbl 0264.49026 · doi:10.1093/imamat/9.1.91
[22] P.E. Gill and W. Murray, ”Quasi-Newton methods for linearly constrained optimization”, Report NAC 32 (1973), National Physical Laboratory, Teddington.
[23] P.E. Gill and W. Murray, ”Newton-type methods for unconstrained and linearly constrained optimization”,Mathematical Programming 7 (1974) 311–350. · Zbl 0297.90082 · doi:10.1007/BF01585529
[24] P.E. Gill and W. Murray, ”Safeguarded steplength algorithms for optimization using descent methods”, Report NAC 37 (1974), National Physical Laboratory, Teddington.
[25] P.E. Gill and W. Murray, eds.,Numerical methods for constrained optimization (Academic Press, London, 1974). · Zbl 0275.90035
[26] P.E. Gill and W. Murray, ”Linearly constrained optimization including quadratic and linear programming”, in: Jacobs and Scriven, eds.,Modern numerical analysis (Academic Press, London, 1977), Proceedings of conference on ”State of the art of numerical analysis”, University of York (April 1976).
[27] P.E. Gill, W. Murray and S.M. Picken, ”The implementation of two modified Newton algorithms for linearly constrained optimization” (to appear).
[28] P.E. Gill, W. Murray and R.A. Pitfield, ”The implementation of two revised quasi-Newton algorithms for unconstrained optimization”, Report NAC 11 (1972), National Physical Laboratory, Teddington.
[29] P.E. Gill, W. Murray and M.A. Saunders, ”Methods for computing and modifying the LDV factors of a matrix”,Mathematics of Computation 29 (1975) 1051–1077. · Zbl 0339.65022
[30] D. Goldfarb, ”Extension of Davidon’s variable metric method to maximization under linear inequality and equality constraints”,SIAM Journal of Applied Mathematics 17 (1969) 739–764. · Zbl 0185.42602 · doi:10.1137/0117067
[31] D. Goldfarb, ”On the Bartels–Golub decomposition for linear programming bases”, AERE Report C.S.S. 18 (1975), Harwell, England. · Zbl 0379.90070
[32] E. Hellerman and D.C. Rarick, ”Reinversion with the preassigned pivot procedure”,Mathematical Programming 1 (1971) 195–216. · Zbl 0246.65022 · doi:10.1007/BF01584086
[33] E. Hellerman and D.C. Rarick, ”The partitioned preassigned pivot procedure”, in: D.J. Rose and R.A. Willoughby, eds.,Sparse matrices and their applications (Plenum Press, New York, 1972) pp. 67–76. · Zbl 0246.65022
[34] D.M. Himmelblau,Applied nonlinear programming (McGraw-Hill, New York, 1972). · Zbl 0241.90051
[35] A. Jain, L.S. Lasdon and M.A. Saunders, ”An in-core nonlinear mathematical programming system for large sparse nonlinear programs”, presented at ORSA/TIMS joint national meeting, Miami, Florida (November, 1976).
[36] J.E. Kalan, ”Aspects of large-scale in-core linear programming”, Proceedings of ACM conference, Chicago (1971) 304–313.
[37] C.E. Lemke, ”Bimatrix equilibrium points and mathematical programming”,Management Science 11 (1965) 681–689. · Zbl 0139.13103 · doi:10.1287/mnsc.11.7.681
[38] A.S. Manne, ”Waiting for the breeder”, The review of economic studies symposium (1974) 47–65.
[39] A.S. Manne, ”U.S. options for a transition from oil and gas to synthetic fuels”, presented at the World Congress of the Econometric Society, Toronto (August 1975).
[40] A.S. Manne, ”ETA: a model for Energy Technology Assessment”,Bell Journal of Economics (Autumn 1976) 381–406.
[41] G.P. McCormick, ”The variable-reduction method for nonlinear programming”,Management Science 17 (3) (1970) 146–160. · Zbl 0209.22803 · doi:10.1287/mnsc.17.3.146
[42] G.P. McCormick, ”A second order method for the linearly constrained nonlinear programming problem”, in: J.B. Rosen, O.L. Mangasarian and K. Ritter, eds.,Nonlinear programming (Academic Press, New York, 1970) pp. 207–243. · Zbl 0231.90049
[43] B.A. Murtagh and P.D. Lucas, ”The modelling of energy production and consumption in New Zealand”, IBM (N.Z.) 5 (1975) 3–6.
[44] B.A. Murtagh and R.W.H. Sargent, ”A constrained minimization method with quadratic convergence”, in: R. Fletcher, ed.,Optimization (Academic Press, New York, 1969) pp. 215–246. · Zbl 0214.42401
[45] A. Perry, ”An improved conjugate gradient algorithm”, Technical note (March 1976), Dept. of Decision Sciences, Graduate School of Management, Northwestern University, Evanston, Illinois.
[46] E. Polak,Computational methods in optimization: a unified approach (Academic Press, New York, 1971). · Zbl 0257.90055
[47] M.J. D. Powell, ”Restart procedures for the conjugate gradient method”, AERE Report C.S.S. 24 (1975), Harwell, England. · Zbl 0396.90072
[48] D.C. Rarick, An improved pivot row selection procedure, implemented in the mathematical programming system MPS III, Management Science Systems, Rockville, MA, U.S.A.
[49] R.W.H. Sargent, ”Reduced-gradient and projection methods for nonlinear programming”, in: P.E. Gill and W. Murray, eds.,Numerical methods for constrained optimization (Academic Press, London, 1974) pp. 149–174.
[50] R.W. Sargent and B.A. Murtagh, ”Projection methods for nonlinear programming”,Mathematical Programming 4 (1973) 245–268. · Zbl 0304.90097 · doi:10.1007/BF01584669
[51] M.A. Saunders, ”Large-scale linear programming using the Cholesky factorization”, Report STAN-CS-72-252 (1972), Computer Science Dept., Stanford University, Stanford, CA, U.S.A.
[52] M.A. Saunders, ”A fast, stable implementation of the simplex method using Bartels–Golub updating”, in: J.R. Bunch and D.J. Rose, eds.,Sparse Matrix Computations (Academic Press, New York, 1976) pp. 213–226. · Zbl 0345.65034
[53] B.R. Smith, P.D. Lucas and B.A. Murtagh, ”The development of a New Zealand energy model”,N.Z. Operational Research 4 (2) (1976) 101–117.
[54] J.A. Tomlin, ”On pricing and backward transformation in linear programming”,Mathematical Programming 6 (1974) 42–47. · Zbl 0278.90043 · doi:10.1007/BF01580221
[55] P. Wolfe, ”The simplex method for quadratic programming”,Econometrica 27 (1959) 382–398. · Zbl 0103.37603 · doi:10.2307/1909468
[56] P. Wolfe, ”The reduced gradient method”, unpublished manuscript, The RAND Corporation (June 1962).
[57] P. Wolfe, ”Methods of nonlinear programming”, in: J. Abadie, ed.,Nonlinear programming (North-Holland, Amsterdam, 1967) pp. 97–131. · Zbl 0178.22802
[58] M.J. Wood, ”The February 1975 state of BUILD”, Ministry of Works and Development report (February 1975), Wellington, New Zealand.
[59] P.E. Gill, W. Murray, S.M. Picken, H.M. Barber and M.H. Wright, Subroutine LNSRCH, NPL Algorithms Library, Reference No. E4/16/0/Fortran/02/76 (February 1976).
[60] J.A. Tomlin, ”Robust implementation of Lemke’s method for the linear complementarity problem”, Technical Report SOL 76-24, Systems Optimization Laboratory, Stanford University (September 1976). · Zbl 0378.90055
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