Generalized Lagrange multiplier technique for nonlinear programming
- Y. Evtushenko
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Our aim here is to present numerical methods for solving a general nonlinear programming problem. These methods are based on transformation of a given constrained minimization problem into an unconstrained maximin problem. This transformation is done by using a generalized Lagrange multiplier technique. Such an approach permits us to use Newton's and gradient methods for nonlinear programming. Convergence proofs are provided, and some numerical results are given.
- Evtushenko, Yu. G.,Some Local Properties of Minimax Problems, USSR Computational Mathematics and Mathematical Physics, Vol. 14, No. 3, 1974.
- Evtushenko, Yu. G.,Iterative Methods for Solving Minimax Problems, USSR Computational Mathematics and Mathematical Physics, Vol. 14, No. 5, 1974.
- Polyak, B. T.,Iterative Methods Using Lagrange Multipliers for Solving Extremal Problems with Constraints of the Equation Type, USSR Computational Mathematics and Mathematical Physics, Vol. 10, No. 5, 1970.
- Zangwill, W. T.,Nonlinear Programming, A Unified Approach, Prentice-Hall, Englewood Cliffs, New Jersey, 1969.
- Gantmacher, F. R.,The Theory of Matrices, Vol. 1, Chelsea Publishing Company, New York, New York, 1974.
- Liapunov, M. A.,Problème General de la Stabilité du Mouvement, Annals of Mathematical Studies, No. 17, Princeton University Press, Princeton, New Jersey, 1949.
- Kantarovich, L. V., andAkilov, G. P.,Functional Analysis in Normed Space, The Macmillan Company, New York, New York, 1964.
- Generalized Lagrange multiplier technique for nonlinear programming
Journal of Optimization Theory and Applications
Volume 21, Issue 2 , pp 121-135
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers-Plenum Publishers
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- Nonlinear programming
- max-min problems
- Lagrange multiplier technique
- Newton's method
- Industry Sectors
- Y. Evtushenko (1) (2)
- Author Affiliations
- 1. Computing Center of the USSR, Moscow, USSR
- 2. Physico-Technical Institute, Moscow, USSR