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Algorithms for nonlinear constraints that use Lagrangian functions.(English)Zbl 0383.90092


MSC:

90C30 Nonlinear programming

Cite

References:

[1]D.P. Bertsekas, ”Convergence rate of penalty and multiplier methods”,Proceedings of the 1973 IEEE Conference on Decision and Control (1973) 260–264.
[2]D.P. Bertsekas, ”Combined primal-dual and penalty methods for constrained minimization”,SIAM Journal on Control 13 (1975) 521–544. ·doi:10.1137/0313030
[3]D.P. Bertsekas, ”Multiplier methods: a survey”,Automatica 12 (1976) 133–145. ·Zbl 0321.49027 ·doi:10.1016/0005-1098(76)90077-7
[4]M.C. Biggs, ”Constrained minimization using recursive quadratic programming”, in: L.C.W. Dixon and G.P. Szegö, eds.,Towards global optimization (North-Holland, Amsterdam, 1975) pp. 341–349.
[5]C.G. Broyden, ”The convergence of a class of double-rank minimization algorithms 2. The new algorithm”,Journal of the Institute of Mathematics and its Applications 6 (1970) 222–231. ·Zbl 0207.17401 ·doi:10.1093/imamat/6.3.222
[6]A.G. Buckley, ”An alternate implementation of Goldfarb’s minimization algorithm”,Mathematical Programming 8 (1975) 207–231. ·Zbl 0309.90047 ·doi:10.1007/BF01580443
[7]J.D. Buys, ”Dual algorithms for constrained optimization”, Ph.D. thesis, University of Leiden (Bronder-Offset, Rotterdam, 1972).
[8]J.E. Dennis and J.J. Moré, ”Quasi-Newton methods, motivation and theory”,SIAM Review 19 (1977) 46–89. ·Zbl 0356.65041 ·doi:10.1137/1019005
[9]R. Fletcher, ”A new approach to variable metric algorithms”,The Computer Journal 13 (1970) 317–322. ·Zbl 0207.17402 ·doi:10.1093/comjnl/13.3.317
[10]R. Fletcher, ”Methods related to Lagrangian functions”, in: P.E. Gill and W. Murray, eds.,Numerical methods for constrained optimization (Academic Press, London, 1974) pp. 219–239.
[11]R. Fletcher, ”An ideal penalty function for constrained optimization”,Journal of the Institute of Mathematics and its Applications 15 (1975) 319–342. ·Zbl 0325.90056 ·doi:10.1093/imamat/15.3.319
[12]R. Fletcher, ”The quest for a natural metric”, presented at the ninth international symposium on mathematical programming, (Budapest, 1976).
[13]U.M. Garcia-Palomares and O.L. Mangasarian, ”Superlinearly convergent quasi-Newton algorithms for nonlinearly constrained optimization problems”,Mathematical Programming 11 (1976) 1–13. ·Zbl 0362.90103 ·doi:10.1007/BF01580366
[14]S-P. Han, ”Penalty Lagrangian methods in a quasi-Newton approach”, Report TR 75-252, Computer Science, Cornell University (Ithaca, 1975).
[15]S-P. Han, ”A globally convergent method for nonlinear programming”, Report TR 75-257, Computer Science, Cornell University (Ithaca, 1975).
[16]S-P. Han, ”Superlinearly convergent variable metric algorithms for general nonlinear programming problems”,Mathematical Programming 11 (1976) 263–282. ·Zbl 0364.90097 ·doi:10.1007/BF01580395
[17]M.R. Hestenes, ”Multiplier and gradient methods”,Journal of Optimization Theory and its Applications 4 (1969) 303–320. ·Zbl 0174.20705 ·doi:10.1007/BF00927673
[18]G.P. McCormick, ”Second order convergence using a modified Armijo step-size rule for function minimization”, presented at the ninth international symposium on mathematical programming (Budapest, 1976).
[19]J.M. Ortega and W.C. Rheinboldt,Iterative solution of nonlinear equations in several variables (Academic Press, New York, 1970). ·Zbl 0241.65046
[20]M.J.D. Powell, ”A method for nonlinear constraints in minimization problems”, in: R. Fletcher, ed.,Optimization (Academic Press, London, 1969) pp. 283–298. ·Zbl 0194.47701
[21]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
[22]R.T. Rockafellar, ”New applications of duality in convex programming”, presented at the seventh international symposium on mathematical programming (The Hague, 1970).
[23]R.T. Rockafellar, ”A dual approach to solving nonlinear programming problems by unconstrained optimization”,Mathematical Programming 5 (1973) 354–373. ·Zbl 0279.90035 ·doi:10.1007/BF01580138
[24]J.B. Rosen and J. Kreuser, ”A gradient projection algorithm for nonlinear constraints”, in: F.A. Lootsma, ed.,Numerical methods for nonlinear optimization (Academic Press, London, 1972) pp. 297–300. ·Zbl 0267.90077
[25]D.M. Ryan, ”Penalty and barrier functions”, in: P.E. Gill and W. Murray, eds.,Numerical methods for constrained optimization (Academic Press, London, 1974) pp. 175–190.
[26]R.W.H. Sargent, ”Reduced-gradient and projection methods for nonlinear programming”, in: P.E. Gill and W. Murray, eds.,Numerical methods for constrained optimization (Academic Press, London, 1974) pp. 149–174.
[27]R.A. Tapia, ”Diagonalized multiplier methods and quasi-Newton methods for constrained optimization”, manuscript (Rice University, Houstoń, 1976). ·Zbl 0336.65034
[28]R.B. Wilson, ”A simplical method for convex programming”, Ph.D. thesis, Harvard University (Cambridge, MA, 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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