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Quasi-Newton methods without projections for linearly constrained minimization. (English) Zbl 0514.65048

MSC:
65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
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References:
[1] J. T. Betts: An accelerated multiplier method for nonlinear programming. J. Optim. Theory Appl. 21 (1977), 2, 137-174. · Zbl 0325.65027 · doi:10.1007/BF00932517
[2] W. C. Davidon: Optimally conditioned optimization algorithms without line searches. Math. Programming 9 (1975), 1,1-30. · Zbl 0328.90055 · doi:10.1007/BF01681328
[3] P. E. Gill W. Murray: A numerically stable form of the simplex algorithm. Linear Algebra Appl. 7 (1973), 2, 99-138. · Zbl 0255.65029 · doi:10.1016/0024-3795(73)90047-5
[4] P. E. Gill W. Murray: Newton-type methods for unconstrained and linearly constrained optimization. Math. Programming 7 (1974), 3, 311 - 350. · Zbl 0297.90082 · doi:10.1007/BF01585529
[5] D. Goldfarb: Extension of Davidon’s variable metric method to maximization under inequality and equality linear constraints. SIAM J. Appl. Math. 17 (1969), 4, 739-764. · Zbl 0185.42602 · doi:10.1137/0117067
[6] L. Lukšan: Quasi-Newton methods without projections for unconstrained minimization. Kybernetika 18 (1892), 4, 290-306.
[7] K. Ritter: A variable metric method for linearly constrained minimization problems. Nonlinear Programming 3 (O. L. Mangasarian, R. R. Meyer, S. M. Robinson. Academic Press, London 1978. · Zbl 0464.65041
[8] W. Hock K. Schittkowski: Test Examples for Nonlinear Programming Codes. (Lecture Notesin Economics and Mathematical Systems 187.) Springer - Verlag, Berlin-Heidelberg-New York 1981. · Zbl 0452.90038
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