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Multiplier methods: A survey.(English)Zbl 0321.49027


MSC:

49M30 Other numerical methods in calculus of variations (MSC2010)
49-02 Research exposition (monographs, survey articles) pertaining to calculus of variations and optimal control

Cite

References:

[1]Mathematical Programming, 5, 225-234 (1973) ·Zbl 0276.90055
[2]Arrow, K. J.; Hurwicz, L.; Uzawa, H., Studies in Linear and Nonlinear Programming (1958), Stanford University Press: Stanford University Press CA ·Zbl 0091.16002
[3]SIAM J. Control, 14 (1976) ·Zbl 0324.49029
[4]D. P. BertsekasProc. 1973 IEEE Conf. on Decision and Control;D. P. BertsekasProc. 1973 IEEE Conf. on Decision and Control
[5]Bertsekas, D. P., On penalty and multiplier methods for constrained minimization, (Mangasarian, O.; Meyer, R.; Robinson, S., Nonlinear Programming 2 (1975), Academic Press: Academic Press New York), 165-191 ·Zbl 0322.90054
[6]Bertsekas, D. P., On the method of multipliers for convex programming, IEEE Trans. Aut. Control, AC-20, 385-388 (1975) ·Zbl 0301.49023
[7]Bertsekas, D. P., Combined primal-dual and penalty methods for constrained minimization, SIAM J. Control, 13, 521-544 (1975) ·Zbl 0269.90044
[8]Math. Programming, 9, 87-99 (1975) ·Zbl 0325.90055
[9](Balinski, M.; Wolfe, P., Mathematical Programming Study 3 (1975), North-Holland) ·Zbl 0335.00010
[10]Bertsekas, D. P., Approximation procedures based on the method of multipliers (January 1976), Coordinated Science Lab. Working Paper, University of Illinois: Coordinated Science Lab. Working Paper, University of Illinois Urbana, IL
[11]Bertsekas, D. P., A general method for approximation based on the method of multipliers, (Proc. of Thirteenth Annual Allerton Conf. on Circuit and System Theory. Proc. of Thirteenth Annual Allerton Conf. on Circuit and System Theory, Allerton Park, IL (October (1975))) ·Zbl 0346.90046
[12]Bertsekas, D. P., A new algorithm for analysis of nonlinear resistive networks, (Proc. of Thirteenth Annual Conf. on Circuit and System Theory. Proc. of Thirteenth Annual Conf. on Circuit and System Theory, Allerton Park, IL (October (1975))) ·Zbl 0788.90055
[13]Buys, J. D., Dual algorithms for constrained optimization, (Ph.D. Thesis (1972), Rijksuniversiteit de Leiden) ·Zbl 0195.17403
[14]Brusch, R. B., A rapidly convergent method for equality constrained function minimization, (Proc. of 1973 IEEE Conf. on Decision and Control (1973)), 80-81
[15]Budak, B. M.; Berkovich, E. M.; Solv’eva, E. N., Difference approximations in optimal control problems, SIAM J. Control, 7, 18-31 (1969) ·Zbl 0175.10501
[16]Cullum, J., Perturbations of optimal control problems, SIAM J. Control, 4, 473-487 (1966) ·Zbl 0152.09202
[17]Cullum, J., Discrete approximations to continuous optimal control problems, SIAM J. Control, 7, 32-49 (1969) ·Zbl 0175.10502
[18]Cullum, J., An explicit method for discretizing continuous optimal control problems, J. Opt. Theory Appl., 8, 15-34 (1971) ·Zbl 0206.15602
[19]Cullum, J., Finite-dimensional approximations of state-constrained continuous optimal control problems, SIAM J. Control, 10, 649-670 (1972) ·Zbl 0244.49018
[20]Daniel, J. W., On the convergence of a numerical method for optimal control problems, J. Opt. Theory Appl., 4, 330-342 (1969) ·Zbl 0174.20704
[21]Fiacco, A. V.; McCormick, G. P., Nonlinear Programming: Sequential Unconstrained minimization Techniques (1968), Wiley: Wiley New York ·Zbl 0193.18805
[22]Fletcher, R., A class of methods for nonlinear programming with termination and convergence properties, (Abadie, J., Integer and Nonlinear Programming (1970), North-Holland: North-Holland Amsterdam) ·Zbl 0332.90039
[23]Fletcher, R.; Lill, S., A class of methods for nonlinear programming: II. Computational experience, (Rosen, J. B.; Mangasarian, O. L.; Ritter, K., Nonlinear Programming (1971), Academic Press: Academic Press New York) ·Zbl 0258.90044
[24]Fletcher, R., A class of methods for nonlinear programming: III. Rates of convergence, (Lootsma, F. A., Numerical Methods for Nonlinear Optimization (1973), Academic Press: Academic Press New York) ·Zbl 0277.90066
[25]Fletcher, R., An ideal penalty function for constrained optimization, (Mangasarian, O.; Meyer, R.; Robinson, S., Nonlinear Programming 2 (1975), Academic Press: Academic Press New York), 121-163 ·Zbl 0322.90053
[26]Gol’shtein, E. G.; Tret’yakov, N. V., Modified Lagrangian functions, Economics Math. Methods, 10, 3, 568-591 (1974), In Russian
[27]Gabay, D.; Mercier, B., A dual algorithm for the Solution of Nonlinear Variational Problems via Finite Element Approximation, IRIA-LABORIA Research Report No. 126 (1975)
[28]Hestenes, M. R., Multiplier and gradient methods, J. Opt. Theory Appl., 4, 303-320 (1969) ·Zbl 0174.20705
[29]Haarhoff, P. C.; Buys, J. D., A new method for the optimization of a nonlinear function subject to nonlinear constraints, Comput. J., 13, 178-184 (1970) ·Zbl 0195.17403
[30]Han, S. P., (Penalty Lagrangian Methods via a Quasi-Newton Approach. Dept. of Computer Science, TR 75-252 (July 1975), Cornell University: Cornell University Ithaca, New York)
[31]B. W. KortD. P. BertsekasProc. 1972 IEEE Conf. on Decision and Control;B. W. KortD. P. BertsekasProc. 1972 IEEE Conf. on Decision and Control
[32]SIAM J. Control, 14 (1976) ·Zbl 0332.90035
[33]B. W. KortD. P. BertsekasProc. 1973 IEEE Conf. on Decision and Control;B. W. KortD. P. BertsekasProc. 1973 IEEE Conf. on Decision and Control
[34]Kort, B. W., Rate of convergence of the method of multipliers with inexact minimization, (Mangasarian, O.; Meyer, R.; Robinson, S., Nonlinear Programming 2 (1975), Academic Press: Academic Press New York), 193-214 ·Zbl 0349.90097
[35]Kort, B. W., Combined Primal-Dual and Penalty Function Algorithms for Nonlinear Programming, (Ph.D. Thesis (1975), Stanford Univ: Stanford Univ Palo Alto, CA)
[36]Klessig, R.; Polak, E., An adaptive precision gradient method for optimal control, SIAM J. Control, 11, 80-93 (1973) ·Zbl 0254.49040
[37]Luenberger, D. G., Introduction to Linear and Nonlinear Programming (1973), Addison-Wesley: Addison-Wesley Reading, MA ·Zbl 0241.90052
[38]Lasdon, L., Optimization Theory for Large Systems (1970), Macmillan: Macmillan New York ·Zbl 0224.90038
[39]Luenberger, D. G., Optimization by Vector Space Methods (1969), Wiley: Wiley New York ·Zbl 0176.12701
[40]Mangasarian, O. L., Unconstrained Lagrangians in nonlinear programming, SIAM J. Control, 13, 772-791 (1975) ·Zbl 0269.90045
[41]Mangasarian, O. L., Unconstrained methods in optimization, (Proc. of Twelfth Allerton Conf. on Circuit and System Theory (October 1974), Univ. of Illinois: Univ. of Illinois Urbana, Ill), 153-160 ·Zbl 0341.90049
[42]Martensson, K., (New Approaches to the Numerical Solution of Optimal Control Problems. Rep. 1206 (1972), Lund Inst. of Tech., Division of Automatic Control: Lund Inst. of Tech., Division of Automatic Control Lund, Sweden)
[43]Martensson, K., A new approach to constrained function optimization, J. Opt. Theory Appl., 12, 531-554 (1973) ·Zbl 0253.49024
[44]Miele, A.; Moseley, P. E.; Levy, A. V.; Coggins, G. M., On the method of multipliers for mathematical programming problems, J. Opt. Theory Appl., 10, 1-33 (1972) ·Zbl 0236.90063
[45]Miele, A.; Moseley, P. E.; Cragg, E. E., A modification of the method of multipliers for mathematical programming problems, (Balakrishnan, A. V., Techniques of Optimization (1972), Academic Press: Academic Press New York) ·Zbl 0269.49042
[46]Miele, A.; Cragg, E. E.; Iyer, R. R.; Levy, A. V., Use of the augmented penalty function in mathematical programming problems, Part I, J. Opt. Theory Appl., 8, 115-130 (1971) ·Zbl 0215.59102
[47]Miele, A.; Cragg, E. E.; Levy, A. V., Use of the augmented penalty function in mathematical programming problems, Part II, J. Opt. Theory Appl., 8, 131-153 (1971) ·Zbl 0208.45803
[48]Mukai, H.; Polak, E., A Quadratically Convergent primal-dual algorithm with global convergence properties for solving optimization problems with equality constraints, Mathematical Programming, 9, 336-349 (1975) ·Zbl 0351.90065
[49]Newell, J. S.; Himmelblau, D. M., Nonlinear programming via a new penalty function, (Presented at Nonlinear Programming Symposium. Presented at Nonlinear Programming Symposium, Madison, Wisc. (1974))
[50]Nakayama, H.; Sayama, H.; Sawaragi, Y., Multiplier method and optimal control problems with terminal state constraints, International Journal of Systems Science, 6, 465-477 (1975) ·Zbl 0297.49034
[51]Nahra, J. E., Balance function for the optimal control problems, J. Opt. Theory Appl., 8, 35-48 (1971) ·Zbl 0206.15604
[52]Polak, E., Computational Methods in Optimization (1971), Academic Press: Academic Press New York ·Zbl 0257.90055
[53]Polyak, V. T.; Tret’yakov, N. V., The method of penalty estimates for conditional extremum problems, USSR Computational Mathematics and Mathematical Physics, 13, 42-58 (1974) ·Zbl 0273.90055
[54]Powell, M. J.D., A method for nonliner constraints in minimization problems, (Fletcher, R., Optimization (1969), Academic Press: Academic Press New York), 283-298 ·Zbl 0881.65003
[55]Polyak, B. T., Gradient methods for the minimization of functionals, Z. Vycisl. Mat. i Mat. Fiz., 3, 643-653 (1963), (Translated inUSSR Computational Mathematics and Mathematical Physics.) ·Zbl 0196.47701
[56]Pollatschek, M. A., Generalized duality theory in nonlinear programming, (Operations Res. Statistics and Economics (1973), Technion: Technion Haifa, Istael), Mimeo Ser. 122 ·Zbl 0916.90274
[57]Polyak, B. T., Iterative methods using Lagrange multipliers for solving extremal problems with constraints of the equation type, Z. Vycisl. Mat. i Mat. Fiz., 10, 1098-1106 (1970), (Translated inUSSR Computational Mathematics Mathematical Physics.) ·Zbl 0217.27501
[58]Polyak, B. T.; Tret’yakov, N. V., On an iterative method of linear programming and its economic interpretation, Economics Math. Methods, 8, 740-751 (1972), (In Russian.)
[59]Rockafellar, R. T., New applications of duality in convex programming, (7th International Symposium on Math. Programming. 7th International Symposium on Math. Programming, The Hague (1970). 7th International Symposium on Math. Programming. 7th International Symposium on Math. Programming, The Hague (1970), Proc. 4th Conf. on Probability, Brasov, Romania (1971)), Published in ·Zbl 0231.90037
[60]Rockafellar, R. T., A Dual Approach to Solving Nonlinear Programming Problems by Unconstrained Optimization, Math. Programming, 5, 354-373 (1973) ·Zbl 0279.90035
[61]Rockafellar, R. T., The multiplier method of Hestenes and Powell applied to convex programming, J. Opt. Theory Appl., 12, 555-562 (1973) ·Zbl 0254.90045
[62]Rockafellar, R. T., Augmented Lagrange multiplier functions and duality in nonconvex programming, SIAM J. Control, 12, 268-285 (1974) ·Zbl 0257.90046
[63]Rockafellar, R. T., Penalty methods and augmented Lagrangians in nonlinear programming, (Proc. 5th IFIP Conf. on Optimization Techniques. Proc. 5th IFIP Conf. on Optimization Techniques, Rome (1973) (1974), Springer-Verlag) ·Zbl 0458.90050
[64]R. T. RockafellarSymposia Mathematica;R. T. RockafellarSymposia Mathematica
[65]Rockafellar, R. T., Convex Analysis (1970), Princeton University Press: Princeton University Press Princeton, N.J ·Zbl 0229.90020
[66]Rupp, R. D., Approximation of the classical isoperimetric problem, J. Opt. Theory Appl., 9, 251-264 (1972) ·Zbl 0217.46802
[67]Rupp, R. D., A method for solving a quadratic optimal control problem, J. Opt. Theory Appl., 9, 238-250 (1972) ·Zbl 0218.49013
[68]Rupp, R. D., A nonlinear optimal control minimization technique, Trans. Am. Math. Soc., 178, 357-381 (1973) ·Zbl 0273.49049
[69]Sayama, H.; Kameyama, Y.; Nakayama, H.; Sawaragi, Y., The Generalized Lagrangian Functions for Mathematical Programming Problems. Kansas State University Report (February (1974))
[70]Tripathi, S. S.; Narendra, K. S., Constrained Optimization Problems Using Multiplier Methods, J. Opt. Theory and Appl., 9, 59-70 (1972) ·Zbl 0213.15702
[71]Tret’yakov, N. V., The method of penalty estimates for problems of convex programming, Economics Math. Methods, 9, 525-540 (1973), (In Russian.)
[72]Wierzbicki, A. P., A penalty function shifting method in constrained static optimization and its convergence properties, Archiwum Automatyki i Telemechaniki, 16, 395-416 (1971) ·Zbl 0227.90045
[73]Wierzbicki, A. P.; Kurcyusz, S., Projection on a Cone, Generalized Penalty Functionals and Duality Theory. Institute of Automatic Control, Technical Univ. of Warsaw, Report No. 1/1974 (February (1974))
[74]Zangwill, W., Nonlinear Programming: A Unified Approach (1969), Prentice-Hall: Prentice-Hall New York ·Zbl 0195.20804
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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