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The multiplier method of Hestenes and Powell applied to convex programming. (English) Zbl 0254.90045

MSC:
90C25 Convex programming
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[1] Hestenes, M. R.,Multiplier and Gradient Methods, Computing Methods in Optimization Problems?2, Edited by L. A. Zadeh, L. W. Neustadt, and A. V. Balakrishnan, Academic Press, New York, New York, 1969.
[2] Hestenes, M. R.,Multiplier and Gradient Methods, Journal of Optimization Theory and Applications, Vol. 4, pp. 303-320, 1969. · Zbl 0174.20705 · doi:10.1007/BF00927673
[3] Powell, M. J. D.,A Method for Nonlinear Constraints in Minimization Problems, Optimization, Edited by R. Fletcher, Academic Press, New York, New York, 1972.
[4] Miele, A., Cragg, E. E., Iver, R. R., andLevy, A. V.,Use of the Augmented Penalty Function in Mathematical Programming Problems, Part 1, Journal of Optimization Theory and Applications, Vol. 8, pp. 115-130, 1971. · Zbl 0215.59102 · doi:10.1007/BF00928472
[5] Miele, A., Cragg, E. E., andLevy, A. V.,Use of the Augmented Penalty Function in Mathematical Programming Problems, Part 2, Journal of Optimization Theory and Applications, Vol. 8, pp. 131-153, 1971. · Zbl 0215.59103 · doi:10.1007/BF00928473
[6] Miele, A., Moseley, P. E., andCragg, E. E.,A Modification of the Method of Multipliers for Mathematical Programming Problems, Techniques of Optimization, Edited by A. V. Balakrishnan, Academic Press, New York, New York, 1972. · Zbl 0226.90041
[7] Miele, A., Moseley, P. E., Levy, A. V., andCoggins, G. M.,On the Method of Multipliers for Mathematical Programming Problems, Journal of Optimization Theory and Applications, Vol. 10, pp. 1-33, 1972. · Zbl 0236.90063 · doi:10.1007/BF00934960
[8] Fletcher, R.,A Class of Methods for Nonlinear Programming with Termination and Convergence Properties, Integer and Nonlinear Programming, Edited by J. Abadie, North-Holland Publishing Company, Amsterdam, Holland, 1970. · Zbl 0332.90039
[9] Fletcher, R., andLill, S. A.,A Class of Methods for Nonlinear Programming, II: Computational Experience, Nonlinear Programming, Edited by J. B. Rosen, O. L. Mangasarian, and K. Ritter, Academic Press, New York, New York, 1971.
[10] Arrow, K. J., andSolow, R. M.,Gradient Methods for Constrained Maxima, with Weakened Assumptions, Studies in Linear and Nonlinear Programming, Edited by K. Arrow, L. Hurwicz, and H. Uzawa, Stanford University Press, Stanford, California, 1958.
[11] Rockafellar, R. T.,A Dual Approach to Solving Nonlinear Programming Problems by Unconstrained Optimization, Mathematical Programming (to appear). · Zbl 0279.90035
[12] Arrow, K. J., Gould, F. J., andHowe, S. M.,A General Saddle Point Result for Constrained Optimization, Mathematical Programming (to appear). · Zbl 0276.90055
[13] Moreau, J. J.,Proximité et Dualité dans un Espace Hilbertien, Bulletin de la Societé Mathématique de France, Vol. 93, pp. 273-279, 1965.
[14] Fan, K., Glicksberg, I., andHoffman, A. J.,Systems of Inequalities Involving Convex Functions, Proceedings of the American Mathematical Society, Vol. 8, pp. 617-622, 1957. · Zbl 0079.02002 · doi:10.1090/S0002-9939-1957-0087574-2
[15] Rockafellar, R. T.,Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970. · Zbl 0193.18401
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