Optimization of the Shape of the Pareto Set in the Problems of Multi-criterial Programming
https://doi.org/10.26794/2308-944X-2018-6-1-5-16
Abstract
In this paper, a scheme for using the method of smooth penalty functions for the dependence of solutions of multi-criterial optimization problems on parameters is being considered. In particular, algorithms based on the method of smooth penalty functions are given to solve problems of optimization by the parameters of the level of consistency of the objective functions and to find the corresponding shape of the Pareto’s set.
About the Authors
B. A. Katendi
Moscow Institute of Physics and Technology (State University)
Russian Federation
Russian Federation
E. A. Umnov
Moscow Institute of Physics and Technology (State University)
Russian Federation
Russian Federation
A. E. Umnov
Moscow Institute of Physics and Technology (State University)
Russian Federation
Russian Federation
References
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3. Umnov, A. E. (1975). Metod shtrafnykh funktsii v zadachakh bol’shoi razmernosti [The method of penalty functions in problems of large dimension]. Zhurnal vychislitel’noi matematiki i matematicheskoi fiziki, 15(6), pp. 1451-1463
4. Zhadan, V. G. (2014). Metody optimizatsii. Chast’ 1. Vvedenie v vypuklyi analiz i teoriyu optimizatsii [Methods of optimization. Part 1. Introduction to convex analysis and optimization theory]. Moskva, Rossiâ: MFTI
5. ,2 Московский физико-технический институт (Государственный университет), Москва, Россия
Review
For citations:
Katendi B.A., Umnov E.A., Umnov A.E. Optimization of the Shape of the Pareto Set in the Problems of Multi-criterial Programming. Review of Business and Economics Studies. 2018;6(1):5-16. (In Russ.) https://doi.org/10.26794/2308-944X-2018-6-1-5-16
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