×

Algorithm model for penalty functions-type iterative pcedures. (English) Zbl 0298.65043


MSC:

65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] E. J. Beltrami; E. J. Beltrami
[2] Butler, T.; Martin, A. V., On a method of courant for minimizing functionals, J. Math. Phys., 41, 291-299 (1962) · Zbl 0116.08001
[3] Canon, M. D.; Cullum, C. D.; Polak, E., Theory of Optimal Control and Mathematical Programming (1970), McGraw-Hill Inc. · Zbl 0264.49001
[4] Courant, R., Variational methods for the solution of problems of equilibrium and vibrations, Bull. Amer. Math. Soc., 49, 1-23 (1943) · Zbl 0810.65100
[5] Cullum, J., Penalty functions and nonconvex continuous optimal control problems, (Computing Methods in Optimization Problems. 2 (1969), Academic Press), 55-67 · Zbl 0192.51804
[6] Dunford, N.; Schwartz, J. T., Linear Operators (1957), Interscience: Interscience New York
[7] Fiacco, A. V.; McCormick, G. P., The sequential unconstrained minimization techniques for nonlinear programming: A primal dual method, Management Sci., 10, 360-364 (1964)
[8] A. V. Fiacco and G. P. McCormick; A. V. Fiacco and G. P. McCormick · Zbl 0193.18805
[9] Frank, M.; Wolfe, P., An algorithm for quadratic programming, Naval Res. Logist Quart., 3, 95-110 (1956)
[10] Kortanek, K. O.; Evans, J. P., Asymptotic Lagrange regularity for pseudoconcave programming with weak constraint qualification, Operation Res., 16, No. 4 (1968) · Zbl 0164.19801
[11] E. S., Levitin; Polyak, B. T., Constrained minimization methods, USSR Comp. Math. and Math. Phys., 6, 1-50 (1966), (Translation of Zh. Vychisl. Mat. i. Mat. Fiz.6 (1966), 787-823.) · Zbl 0184.38902
[12] Meyer, G. G.L., Abstract Models for the Synthesis of Optimization Algorithms, (Ph.D. Thesis (June 1970), Department of Electrical Engineering, University of California: Department of Electrical Engineering, University of California Berkeley) · Zbl 0209.16704
[13] Meyer, G. G.L.; Polak, E., Abstract models for the synthesis of optimization algorithms, SIAM J. Control, 9, 547-559 (1970) · Zbl 0209.16704
[14] Meyer, G. G.L., An open loop method of feasible directions for the solution of optimal control problems, (Proceedings of the Sixth Annual Princeton Conference on Information Sciences and Systems (1972)) · Zbl 0323.65022
[15] Meyer, G. G.L., A drivable method of feasible directions, SIAM J. Control, 11, 113-118 (1973) · Zbl 0255.90052
[16] Meyer, R., The validity of a family of optimization methods, SIAM J. Control, 8, 41-54 (1970) · Zbl 0194.20501
[17] Michael, E., Topologies on spaces of subsets, Amer. Math. Soc. Trans., 71, 152-182 (1951) · Zbl 0043.37902
[18] Polak, E., On the convergence of optimization algorithms, Rev. Française Informat. Recherche Operationnelle, Serie Rouge, 16, 17-34 (1969) · Zbl 0174.47906
[19] Polyak, B. T., Gradient methods for the minimization of functionals, U.S.S.R. Comput. Math. and Math. Phys., 3, 864-878 (1963), (Translation of Zh. Vychisl. Mat. i. Mat. Fiz.3 (1963), 643-653.) · Zbl 0196.47701
[20] Russell, D. L., Penalty functions and bounded phase coordinate control, SIAM J. Control, 2, 409-422 (1965) · Zbl 0133.36802
[21] Topkis, D. M.; Veinott, A., On the convergence of some feasible directions algorithms for nonlinear programming, SIAM J. Control, 5, 286-379 (1967)
[22] Warga, J., Relaxed variational problems, J. Math. Anal. Appl., 4, 111-128 (1962) · Zbl 0102.31801
[23] Yosida, K., Functional Analysis (1968), Springer-Verlag: Springer-Verlag New York · Zbl 0152.32102
[24] Zangwill, W. I., Convergence Conditions for Nonlinear Programming Algorithms, (Working Paper No. 196 (November 1966), Center for Research in Management Science, University of California, Berkeley) · Zbl 0191.49101
[25] Zangwill, W. I., Nonlinear Programming: A Unified Approach (1969), Prentice Hall: Prentice Hall Englewood Cliffs, New Jersey · Zbl 0191.49101
[26] Zlobec, S., Asymptotic Kuhn—Tucker conditions for mathematical programming problems in a Banach space, SIAM J. Control, 8, 505-512 (1970) · Zbl 0206.49003
[27] Zoutendijk, G., Methods of Feasible Directions (1960), Elsevier: Elsevier Amsterdam · Zbl 0097.35408
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.