Generalized Lagrange multiplier technique for nonlinear programming Authors
Cite this article as: Evtushenko, Y. J Optim Theory Appl (1977) 21: 121. doi:10.1007/BF00932516 Abstract
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.
Key Words Nonlinear programming max-min problems Lagrange multiplier technique Newton's method
Communicated by G. Leitmann
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., and Akilov, G. P., Functional Analysis in Normed Space, The Macmillan Company, New York, New York, 1964. Copyright information
© Plenum Publishing Corporation 1977