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A quadratically convergent primal-dual algorithm with global convergence properties for solving optimization problems with equality constraints.(English)Zbl 0351.90065


MSC:

90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
49M30 Other numerical methods in calculus of variations (MSC2010)

Cite

References:

[1]K.J. Arrow and R.M. Solow, ”Gradient methods for constrained maxima with weakened assumptions”, in: K.J. Arrow, L. Hurwicz and H. Uzawa, eds.,Studies in linear and nonlinear programming (Stanford University Press, Stanford, Calif., 1958) pp. 166–176.
[2]D.P. Bertsekas, ”Combined primal-dual and penalty methods for constrained minimization”,SIAM Journal on Control, to appear. ·Zbl 0269.90044
[3]D.P. Bertsekas, ”On penalty and multiplier methods for constrained minimization”,SIAM Journal on Control, to appear. ·Zbl 0324.49029
[4]J.D. Buys, ”Dual algorithm for constrained optimization problems”, Doctoral Dissertation, University of Leiden (June 1972).
[5]R. Fletcher, ”A class of methods for nonlinear programming with termination and convergence properties”, in: J. Abadie, ed.,Integer and nonlinear programming (North-Holland, Amsterdam, 1970) pp. 157–175. ·Zbl 0332.90039
[6]R. Fletcher and S. Lill, ”A class of methods for nonlinear programming II: computational experience”, in: J.B. Rosen, O.L. Mangasarian and K. Ritter, eds.,Nonlinear programming (Academic Press, New York, 1971). ·Zbl 0258.90044
[7]R. Fletcher, ”A class of methods for nonlinear programming III: rate of convergence”, in: F.A. Lootsma, ed.,Numerical methods for nonlinear optimization (Academic Press, New York, 1972). ·Zbl 0277.90066
[8]P.C. Haarhoff and J.D. Buys, ”A new method for the optimization of a nonlinear function subject to nonlinear constraints”,The Computer Journal 13 (1970) 178–184. ·Zbl 0195.17403 ·doi:10.1093/comjnl/13.2.178
[9]M.R. Hestenes, ”The Weierstrass E-function in the calculus of variations”,Transactions of the American Mathematical Society 60 (1946) 51–71. ·Zbl 0063.02001
[10]M.R. Hestenes, ”Multiplier and gradient methods”,Journal of Optimization Theory and Applications 4 (1969) 303–320. ·Zbl 0174.20705 ·doi:10.1007/BF00927673
[11]K. Levenberg, ”A method for the solution of certain nonlinear problems in least squares”,Quarterly of Applied Mathematics 2 (1944) 164–168. ·Zbl 0063.03501
[12]D. Marquardt, ”An algorithm for least squares estimation of nonlinear parameters”,SIAM Journal on Applied Mathematics 11 (1963) 431–441. ·Zbl 0112.10505 ·doi:10.1137/0111030
[13]K. Mârtensson, ”A new approach to constrained function optimization”,Journal of Optimization Theory and Applications 12 (1973) 531–554. ·Zbl 0253.49024 ·doi:10.1007/BF00934776
[14]A. Miele, P.E. Moseley and E.E. Cragg, ”Numerical experiments on Hestenes’ method of multipliers for mathematical programming problems”, Aero-Astronautics Rept. No. 85, Rice University, Houston, Texas (1971). ·Zbl 0232.90056
[15]A. Miele, P.E. Moseley and E.E. Cragg, ”A modification of the method of multipliers for mathematical programming problems”, in: A.V. Balakrishnan, ed.,Techniques of optimization (Academic Press, New York, 1972). ·Zbl 0269.49042
[16]E. Polak, R.W.H. Sargent and D.J. Sebastian, ”On the convergence of sequential minimization algorithms”,Journal of Optimization Theory and Applications 14 (1974) 439–442. ·Zbl 0281.65044 ·doi:10.1007/BF00933310
[17]M.J.D. Powell, ”A method for nonlinear constraints in minimization problems”, in: R. Fletcher, ed.,Optimization (Academic Press, New York, 1969). ·Zbl 0194.47701
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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