Title:
|
A quadratic programming algorithm for large and sparse problems (English) |
Author:
|
Tůma, Miroslav |
Language:
|
English |
Journal:
|
Kybernetika |
ISSN:
|
0023-5954 |
Volume:
|
27 |
Issue:
|
2 |
Year:
|
1991 |
Pages:
|
155-167 |
. |
Category:
|
math |
. |
MSC:
|
90-08 |
MSC:
|
90C06 |
MSC:
|
90C20 |
idZBL:
|
Zbl 0746.90048 |
idMR:
|
MR1106786 |
. |
Date available:
|
2009-09-24T18:24:15Z |
Last updated:
|
2012-06-05 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/124517 |
. |
Reference:
|
[1] R. G. Bland: New finite pivoting rules for the simplex method.Math. Oper. Res. 2 (1977), 103-107. Zbl 0408.90050, MR 0459599 |
Reference:
|
[2] P. H. Calamai, J. J. More: Projected gradient methods for linearly constrained problems.Math. Programming 39 (1987), 93-116. Zbl 0634.90064, MR 0909010 |
Reference:
|
[3] T. F. Coleman: Large Sparse Numerical Optimization.(Lecture Notes in Computer Science 165.) Springer-Verlag, Berlin-Heidelberg-New York-Tokyo 1984. Zbl 0536.65047, MR 0743750 |
Reference:
|
[4] R. S. Dembo: NLPNET - User's Guide and System Documentation.School of Organiza- tion and Management Working Paper Series B # 70, Yale University, New Haven, CT 1983. |
Reference:
|
[5] R. S. Dembo: A primal truncated Newton algorithm with application to large-scale nonlinear network optimization.Math. Programming Study 31 (1987), 43-71. Zbl 0635.90072, MR 0903204 |
Reference:
|
[6] R. S. Dembo S. C. Eisenstat, T. Steihaug: Inexact Newton methods.SIAM J. Numer. Anal. 79(1982), 400-408. MR 0650059 |
Reference:
|
[7] R. S. Dembo, J. G. Klincewicz: Dealing with degeneracy in reduced gradient algorithms.Math. Programming 31 (1985), 357-363. Zbl 0573.90083, MR 0783400 |
Reference:
|
[8] R. S. Dembo, T. Sahi: A convergent active-set strategy for linearly-constrained optimization.School of Organization and Management Working Paper Series B # 80, Yale University 1984. |
Reference:
|
[9] R. S. Dembo, T. Steihaug: Truncated-Newton algorithms for large-scale unconstrained optimization.Math. Programming 26 (1983), 190-212. Zbl 0523.90078, MR 0700647 |
Reference:
|
[10] A. Drud: CONOPT: A GRG code for large sparse dynamic nonlinear optimization problems.Math. Programming 31 (1985), 153-191. Zbl 0557.90088, MR 0777289 |
Reference:
|
[11] L. F. Escudero: An Algorithm for Large-scale Quadratic Programming and its Extensions to the Linearly Constrained Case.IBM Scientic Centre Report SCR-01.81, Madrid 1981. |
Reference:
|
[12] Y. Fan L. Lasdon, S. Sarkar: Experiments with successive quadratic programming algorithms.J. Optim. Theory Appl. 56 (1988), 359-383. MR 0930214 |
Reference:
|
[13] R. Fletcher: Practical Methods of Optimization.Vol. 2: Constrained Optimization. J. Wiley, New York-Chichester-Brisbane-Toronto 1981. Zbl 0474.65043, MR 0633058 |
Reference:
|
[14] P. E. Gill, W. Murray: Newton-type methods for unconstrained and linearly constrained optimization.Math. Programming 28 (1974), 311 - 350. Zbl 0297.90082, MR 0356503 |
Reference:
|
[15] P. E. Gill, W. Murray: The Computation of Lagrange Multiplier Estimates for Constrained Minimization.Rep. NAC 77, National Physical Laboratory, England 1976. |
Reference:
|
[16] W. Hock, K. Schittkowski: Test Examples for NLP Codes.Springer-Verlag, Berlin-Heidelberg-New York 1981. MR 0611512 |
Reference:
|
[17] L. Luksan: System UFO.User's Guide-version 1989(in Czech). Res. Rep. V-441, SVT CSAV, Prague, 1989. |
Reference:
|
[18] H. M. Markowitz: The elimination form of the inverse and its applications to linear programming.Management Sci. 3 (1957), 225-269. MR 0112244 |
Reference:
|
[19] B. A. Murtagh: Advanced Linear Programming: Computation and Practice.McGraw Hill New York 1981. Zbl 0525.90062, MR 0609151 |
Reference:
|
[20] B. A. Murtagh, M. A. Saunders: Large-scale linearly constrained optimization.Math. Programming 14 (1978), 41 - 72. Zbl 0383.90074, MR 0462607 |
Reference:
|
[21] B. A. Murtagh, M. A. Saunders: A projected Lagrangian algorithm and its implementation for sparse nonlinear constraints.Math. Programming Study 16 (1982), 84-117. Zbl 0477.90069, MR 0650630 |
Reference:
|
[22] B. A. Murtagh, M. A. Saunders: MINOS 5.1 User's Guide.Tech. Rep. SOL 83-20 R, Dept. Oper. Res., Stanford University, Stanford, CA, 1983, revised 1987. |
Reference:
|
[23] O. Osterby, Z. Zlatev: Direct methods for sparse matrices.(Lecture Notes in Computer Science 157.) Springer-Verlag, Berlin -Heidelberg-New York-Tokyo 1983. Zbl 0516.65011, MR 0716136 |
Reference:
|
[24] S. Pissanetzky: Sparse Matrix Technology.Academic Press, London-Orlando-San Die- go-New York-Austin-Toronto-Montreal-Sydney-Tokyo 1984. Zbl 0536.65019, MR 0751237 |
Reference:
|
[25] J. K. Reid: On the method of conjugate gradients for the solution of large sparse systems of linear equations.In: Large Sparse Sets of Linear Equations (J. K. Reid, ed.), Academic Press, London 1971, pp. 231 - 254. MR 0341836 |
Reference:
|
[26] J. K. Reid: Fortran Subroutines for Handling Sparse Linear Programming Bases.Rep. AERE Harwell, R. 8269. Harwell 1976. |
Reference:
|
[27] J. K. Reid: A sparsity-exploiting variant of the Bartels-Golub decomposition for linear programming bases.Math. Programming 24 (1982), 55-69. Zbl 0492.90050, MR 0667939 |
Reference:
|
[28] P. S. Ritch: Discrete optimal control with multiple constraints I: Constraint separation and transformation technique.Automatica 9 (1973), 415-429. Zbl 0256.49034, MR 0439328 |
Reference:
|
[29] M. Tůma: Large and Sparse Quadratic Programming (in Czech).Ph.D. Thesis, SVT CSAV, Prague 1989. |
Reference:
|
[30] M. Tůma: SPOPT-Program System for the Solution of Large Sparse Problems of Linear and Quadratic Programming (in Czech).Res. Rep. V-391, SVT CSAV, Praha 1989. |
Reference:
|
[31] Z. Zlatev: A survey of the advances in the exploitation of the sparsity in the solution of large problems.Internat. Congress on Comp. and Appl. Math., University of Leuven, Belgium 1986. MR 0920380 |
. |