Abstract
In a recent paper (Ref. 1), the author briefly mentioned a variant of Hestenes' method of multipliers which would converge quadratically. This note examines that method in detail and provides some examples. In the quadratic-linear case, this algorithm converges in one iteration.
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References
Rupp, R. D.,On the Combination of the Multiplier Method of Hestenes and Powell with Newton's Method, Journal of Optimization Theory and Applications, Vol. 15, No. 2, 1975.
Hestenes, M. R.,Multiplier and Gradient Methods, Journal of Optimization Theory and Applications, Vol. 4, No. 5, 1969.
Powell, M. J. D.,A Method for Nonlinear Constraints in Minimization Problems, Optimization, Edited by R. Fletcher, Academic Press, New York, New York, 1969.
Bertsekas, D. P.,Combined Primal-Dual and Penalty Methods for Constrained Minimization, SIAM Journal on Control, Vol. 13, No. 3, 1975.
Rockafellar, R. T.,The Multiplier Method of Hestenes and Powell Applied to Convex Programming, Journal of Optimization Theory and Applications, Vol. 12, No. 6, 1973.
Miele, A., Moseley, P. A., Levy, A. V., andCoggins, G. M.,On the Method of Multipliers for Mathematical Programming Problems, Journal of Optimization Theory and Applications, Vol. 10, No. 1, 1972.
Bliss, G. A.,Lectures in the Calculus of Variations, University of Chicago Press, Chicago, Illinois, 1946.
Rupp, R. D.,Convergence and Duality for the Multiplier and Penalty Method, Journal of Optimization Theory and Applications, Vol. 15, No. 1, 1975.
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Communicated by M. R. Hestenes
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Rupp, R.D. Quadratic multiplier method convergence. J Optim Theory Appl 20, 1–12 (1976). https://doi.org/10.1007/BF00933344
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DOI: https://doi.org/10.1007/BF00933344