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On the convergence properties of second-order multiplier methods. (English) Zbl 0362.65041

MSC:
65H10 Numerical computation of solutions to systems of equations
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[1] Bertsekas, D. P.,Multiplier Methods: A Survey, Automatica, Vol. 12, pp. 133-145, 1976. · Zbl 0321.49027 · doi:10.1016/0005-1098(76)90077-7
[2] Bertsekas, D. P.,On Penalty and Multiplier Methods for Constrained Minimization, SIAM Journal on Control and Optimization, Vol. 14, pp. 216-235, 1976. · Zbl 0324.49029 · doi:10.1137/0314017
[3] Tapia, R. A.,Newton’s Method for Optimization Problems with Equality Constraints, SIAM Journal on Numerical Analysis, Vol. 11, pp. 874-886, 1974. · Zbl 0306.90065 · doi:10.1137/0711069
[4] Tapia, R. A.,Diagonalized Multiplier Methods and Quasi-Newton Methods for Constrained Optimization, Journal of Optimization Theory and Applications, Vol. 22, pp. 135-194, 1977. · Zbl 0336.65034 · doi:10.1007/BF00933161
[5] Han, S. P.,Dual Variable Metric Algorithms for Constrained Optimization, SIAM Journal on Control and Optimization, Vol. 15, pp. 546-565, 1977. · Zbl 0361.90074 · doi:10.1137/0315037
[6] Bertsekas, D. P.,Convergence Rate of Penalty and Multiplier Methods, Proceedings of 1973 IEEE Conference on Decision and Control, San Diego, California, pp. 260-264, 1973.
[7] Polyak, V. T., andTretyakov, N. V.,The Method of Penalty Estimates for Conditional Extremum Problems, USSR Computational Mathematics and Mathematical Physics, Vol. 13, pp. 42-58, 1974. · Zbl 0273.90055 · doi:10.1016/0041-5553(74)90004-4
[8] Bertsekas, D. P.,Combined Penalty and Lagrangian Methods for Constrained Optimization, University of Illinois, Urbana, Illinois, Coordinated Science Laboratory, Working Paper, 1977.
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