×

Numerically stable methods for quadratic programming. (English) Zbl 0374.90054


MSC:

90C20 Quadratic programming
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] P. Businger and G.H. Golub, ”Linear least squares solutions by Householder transformations”,Numerische Mathematik 7 (1965) 269–276. · Zbl 0142.11503 · doi:10.1007/BF01436084
[2] A.R. Conn, ”Constrained optimization using a non-differentiable penalty function”,SIAM Journal of the Numerical Analysis 10 (1973) 760–784. · Zbl 0259.90039 · doi:10.1137/0710063
[3] A.R. Conn and J.W. Sinclair, ”Quadratic programming via a non-differentiable penalty function”, Department of Combinations and Optimization Research, University of Waterloo, Rep. CORR 75-15 (1975).
[4] R. Fletcher, ”The calculation of feasible points for linearly constrained optimization problems”, UKAEA Research Group Rept., AERE R6354 (1970).
[5] R. Fletcher and M.P. Jackson, ”Minimization of a quadratic function of many variables subject only to lower and upper bounds”,Journal of the Institute of Mathematics and its Applications 14 (1974) 159–174. · Zbl 0301.90032 · doi:10.1093/imamat/14.2.159
[6] P.E. Gill, ”Numerical methods for large-scale linearly-constrained optimization problems”, Ph.D. thesis, Imperial College of Science and Technology, London University (1975).
[7] P.E. Gill and W. Murray, ”Quasi-Newton methods for linearly-constrained optimization”, in: P.E. Gill and W. Murray, eds.,Numerical methods for constrained optimization (Academic Press, London, 1974) pp. 67–92. · Zbl 0297.90082
[8] P.E. Gill and W. Murray, ”Newton-type methods for linearly-constrained optimization”, in: P.E. Gill and W. Murray, eds.,Numerical methods for constrained optimization (Academic Press, London, 1974) pp. 29–66. · Zbl 0297.90082
[9] 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
[10] P.E. Gill and W. Murray, ”Minimization of a nonlinear function subject to bounds on the variables”, NPL NAC Rep. No. 72 (1976).
[11] P.E. Gill and W. Murray, ”The computation of Lagrange-multiplier estimates for constrained minimization”, NPL NAC Rep. No. 77 (1977). · Zbl 0423.90073
[12] P.E. Gill and W. Murray, ”Linearly-constrained problems including linear and quadratic programming”, in: D. Jacobs, ed.,A survey of numerical analysis–1976, (Academic Press, London, 1977).
[13] 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
[14] C.L. Lawson and R.J. Hanson,Solving least-squares problems (Prentice Hall, Englewood Cliffs, NJ, 1974). · Zbl 0860.65028
[15] W. Murray, ”An algorithm for finding a local minimum of an indefinite quadratic program”, NPL NAC Rep. No. 1 (1971).
[16] J.H. Wilkinson,The algebraic eigenvalue problem (Oxford University Press, London, 1965). · Zbl 0258.65037
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.