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Superlinearly convergent variable metric algorithms for general nonlinear programming problems.(English)Zbl 0364.90097


MSC:

90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
41A25 Rate of convergence, degree of approximation

Cite

References:

[1]K.J. Arrow, F.J. Gould and S.M. Howe, ”A general saddle point result for constrained optimization”,Mathematical Programming 5 (1973) 225–234. ·Zbl 0276.90055 ·doi:10.1007/BF01580123
[2]C.G. Broyden, ”A class of methods for solving nonlinear simultaneous equations”,Mathematics of Computation 19 (1965) 577–593. ·Zbl 0131.13905 ·doi:10.1090/S0025-5718-1965-0198670-6
[3]C.G. Broyden, J.E. Dennis and J.J. Moré, ”On the local and superlinear convergence of quasi-Newton methods”,Journal of the Institute of Mathematics and its Applications 12 (1973) 223–245. ·Zbl 0282.65041 ·doi:10.1093/imamat/12.3.223
[4]A.R. Colville, ”A comparative study on nonlinear programming codes”, IBM New York Scientific Center, Tech. Rept. 320-2949 (1968).
[5]R.W. Cottle, ”The principal pivoting method of quadratic programming”, in: G.B. Dantzig and A.F. Veinott, eds., Mathematics of the decision sciences, part 1. Am. Math. Soc., Providence, R.I., (1968) 144–162. ·Zbl 0196.22902
[6]W.C. Davidon, ”Variable metric method for minimization”, A.E.C. Res. and Dev. Report # ANL-5990 (1959). ·Zbl 0752.90062
[7]J.E. Dennis, ”On some methods based on Broyden’s secant approximation to the Hessian”, in F.A. Lootsma, ed.,Numerical methods for nonlinear optimization (Academic Press, New York 1972) 19–34. ·Zbl 0303.65045
[8]J.E. Dennis and J.J. Moré, ”A characterization of superlinear convergence and its application to quasi-Newton methods”,Mathematics of Computation 28, (126) 1974.
[9]L.C.W. Dixon, ”All the quasi-Newton family generate identical points”,Journal of Optimization Theory and Applications 10 (1972) 34–40. ·Zbl 0226.49014 ·doi:10.1007/BF00934961
[10]A.V. Fiacco and G.P. McCormick,Nonlinear programming: Sequential unconstrained minimization techniques (Wiley, New York, 1968). ·Zbl 0193.18805
[11]R. Fletcher and M.J.D. Powell, ”A rapidly convergent descent method for minimization”,The Computer Journal 6 (1963) 163–168. ·Zbl 0132.11603
[12]U.M. Garcia-Palomares, ”Superlinearly convergent quasi-Newton method for nonlinear programming”, Ph.D. dissertation, University of Wisconsin, Madison, Wisc. (1973).
[13]U.M. Garcia-Palomares and O.L. Mangasarian, ”Superlinearly convergent quasi-Newton algorithms for nonlinearly constrained optimization problems”, Computer Sciences Technical Report # 195, University of Wisconsin, Madison, Wisc. (1974). ·Zbl 0362.90103
[14]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). ·Zbl 0297.90082
[15]D. Goldfarb, ”Extension of Davidon’s variable metric method to maximization under linear and inequality constraints”,SIAM Journal on Applied Mathematics 17 (1969) 739–764. ·Zbl 0185.42602 ·doi:10.1137/0117067
[16]S.P. Han, ”Superlinearly convergent variable metric methods for general nonlinear programming problems”, Ph.D. dissertation, University of Wisconsin, Madison, Wisc. (1974).
[17]S.P. Han, ”Dual variable metric algorithms for constrained optimization”,SIAM Journal on Control and Optimization, to appear. ·Zbl 0361.90074
[18]S.P. Han, ”A globally convergent method for nonlinear programming”,Journal of Optimization Theory and Applications, to appear. ·Zbl 0336.90046
[19]S.P. Han, ”A hybrid method for constrained optimization problems”, in preparation.
[20]L.A. Liusternik and V.J. Sobolev,Elements of functional analysis (Frederick Ungan, New York, 1961).
[21]F.A. Lootsma, ”A survey of methods for solving constrained minimization problems via unconstrained minimization”, in: F.A. Lootsma, ed.,Numerical methods for nonlinear optimization, (Academic Press, New York, 1972) 313–347. ·Zbl 0268.90058
[22]O.L. Mangasarian, Private communication.
[23]J.M. Ortega and W.C. Rheinboldt,Iterative solution of nonlinear equations in several variables (Academic Press, New York, 1970). ·Zbl 0241.65046
[24]J.D. Pearson, ”Variable metric methods of minimization”,The Computer Journal 12 (1969) 171–178. ·Zbl 0207.17301 ·doi:10.1093/comjnl/12.2.171
[25]M.J.D. Powell, ”A new algorithm for unconstrained optimization, in: J.B. Rosen, O.L. Mangasarian and K. Ritter, eds.,Nonlinear programming, (Academic Press, New York, 1970). ·Zbl 0228.90043
[26]M.J.D. Powell, ”A fortran subroutine for unconstrained minimization, requiring first derivatives of the objective functions”, A.E.R.E. Harwell report R64-69 (1970).
[27]S.M. Robinson, ”A quadratically convergent algorithm for general nonlinear programming problems”,Mathematical Programming 3 (1972) 145–156. ·Zbl 0264.90041 ·doi:10.1007/BF01584986
[28]S.M. Robinson, ”Perturbed Kuhn–Tucker points and rates of convergence for a class of nonlinear-programming algorithms”,Mathematical Programming 7 (1974) 1–16. ·Zbl 0294.90078 ·doi:10.1007/BF01585500
[29]R.T. Rockafellar, ”New applications of duality in nonlinear programming”, Symposium on Mathematical Programming. The Hague, September 1970. ·Zbl 0278.90059
[30]G.W. Stewart, ”A modification of Davidon’s minimization method to accept difference approximations of derivatives”,Journal of the Association for Computing Machinery 14 (1967) 72–83. ·Zbl 0239.65056
[31]C. van de Panne,Methods for linear and quadratic programming (North-Holland, Amsterdam, 1975). ·Zbl 0348.90094
[32]R.B. Wilson, ”A simplicial method for concave programming”, Ph.D. dissertation, Harvard University, Cambridge, Mass. (1963).
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.
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