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Prost O’Leary, Dianne

A generalized conjugate gradient algorithm for solving a class of quadratic programming problems. (English) Zbl 0464.65039

Linear Algebra Appl. 34, 371-399 (1980).
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Cited in 37 Documents

MSC:

65K05 Numerical mathematical programming methods
90C20 Quadratic programming
65F35 Numerical computation of matrix norms, conditioning, scaling
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)

Keywords:

sparsity techniques; linear complementarity problem; scaled conjugate gradient method; quadratic function; convergence rate

Citations:

Zbl 0191.490; Zbl 0344.65047
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Full Text: DOI

References:

[1] Axelsson, O., Solution of linear systems of equations: iterative methods, (Barker, V. A., Sparse Matrix Techniques (1977), Springer: Springer New York), 1-11
[2] Baiocchi, C.; Comincioli, V.; Magenes, E.; Pozzi, G. A., Free boundary problems in the theory of fluid flow through porous media, Ann. Mat. Pura. Appl., 97, 1-82 (1973) · Zbl 0343.76036
[3] Cea, J.; Glowinski, R., Sur des methodes d’optimisation par relaxation, R.A.I.R.O., R-3, 5-32 (1953) · Zbl 0279.90033
[4] Concus, Paul; Golub, Gene H.; O’Leary, Dianne P., A generalized conjugate gradient method for the numerical solution of elliptic partial differential equations, (Bunch, James R.; Rose, Donald J., Sparse Matrix Computations (1976), Academic: Academic New York), 309-332 · Zbl 0595.65110
[5] Cottle, Richard W.; Goheen, Mark S., A special class of large quadratic programs, (Report SOL 76-7 (1976), Stanford Univ. Systems Optimization Lab. Stanford: Stanford Univ. Systems Optimization Lab. Stanford Calif) · Zbl 0458.90049
[6] Cottle, Richard W.; Golub, Gene H.; Sacher, Richard, On the solution of large, structured linear complementarity problems: the block partitional case, Appl. Math. Optimization, 4, 347-363 (1978) · Zbl 0391.90087
[7] Cryer, C. W., The method of Christopherson for solving free boundary problems for infinite journal bearings by means of finite differences, Math. Comp., 25, 435-443 (1971) · Zbl 0223.65044
[8] Daniel, J. W., The conjugate gradient method for linear and nonlinear operator equations, SIAM J. Numer. Anal., 4, 10-26 (1967) · Zbl 0154.40302
[9] Dantzig, G. B.; Cottle, R. W., Complementary pivot theory of mathematical programming, (Dantzig, G. B.; Veinott, A. F., Mathematics of the Decision Sciences, Part 1 (1968), Amer. Math. Soc: Amer. Math. Soc Providence, R.I), 115-136 · Zbl 0208.45503
[10] Diamond, Martin A., The solution of a quadratic programming problem using fast methods to solve systems of linear equations, Internat. J. Systems Sci., 5, 131-136 (1974) · Zbl 0297.90065
[11] Fletcher, R.; Jackson, M. P., Minimization of a quadratic function of many variables subject only to lower and upper bounds, J. Inst. Maths. Applics., 14, 159-174 (1974) · Zbl 0301.90032
[12] Forsythe, G. E.; Straus, E. G., On best conditioned matrices, Proc. Am. Math. Soc., 340-345 (1955) · Zbl 0064.37501
[13] Hadley, G., Nonlinear and Dynamic Programming (1964), Addison-Wesley: Addison-Wesley Reading, Mass · Zbl 0179.24601
[14] Hestenes, Magnus R.; Stiefel, Eduard, Methods of conjugate gradients for solving linear systems, J. Res. Nat. Bureau Stand., 49, 409-436 (1952) · Zbl 0048.09901
[15] Lemke, C. E., Bimatrix equilibrium points and mathematical programming, Management Sci., 11, 681-689 (1965) · Zbl 0139.13103
[16] Luenberger, David G., Introduction to Linear and Nonlinear Programming (1965), Addison-Wesley: Addison-Wesley Reading, Mass · Zbl 0297.90044
[17] Meijerink, J. A.; van der Vorst, H. A., An iterative solution method for linear systems of which the coefficient matrix is a symmetric \(M\)-matrix, Math. Comp., 31, 148-162 (1977) · Zbl 0349.65020
[18] Murray, W., An algorithm for finding a local minimum of an indefinite quadratic program, (Report NAC 1 (1971), National Physical Laboratory: National Physical Laboratory Teddington, England)
[19] Polyak, B. T., The conjugate gradient method in extremal problems, U.S.S.R. Computational Mathematics and Mathematical Physics, 9, 94-112 (1969) · Zbl 0229.49023
[20] Sacher, Richard S., On the solution of large, structured linear complementarity problems II, (Report 73-5 (1974), Stanford University Operations Research Department: Stanford University Operations Research Department Stanford, Calif) · Zbl 0375.90048
[21] Wilkinson, J. H., The Algebraic Eigenvalue Problem (1965), Clarendon Press: Clarendon Press Oxford · Zbl 0258.65037
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