Abstract
In applications one has often to tackle extremum problems where the objective function happens to be not strictly fixed as in the general theory of nonlinear programming but changes versus some parameter (time, in particular). That is, instead of F(x) there is a sequence of functions F N(x) in a certain sense approximating F(x), on the basis of which the extremum of F(x) is to be found. As a rule, one fails to execute the passage to the limit, to find and then its extremum due to a number of circumstances of which the following might be emphasized:
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1.
The parameter M corresponds to the discrete time and FN(x) becomes known at the instant t=N only. In this case the limit passage takes a whole time given for the problem solution.
2. The parameter N is an index of members of the sequence. It may be changed at one’s discretion, “frozen”, in particular, at some stages of the optimization process, however, the execution of limit passage is technically difficult.
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References
Yu. M. Ermol’ev, Methods for Solving Nonlinear Extremum Problems, Kibemetika, No. 4, 1966.
E. A. Nurminskiy, Convergence Conditions of Nonlinear Programming Algorithms, Kibernetika, No. 6, 1972.
Yu. M. Ermol’ev, E. A. Nurminskiy, Limit Extremum Problems, Kibernetika, No. 4, 1973.
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© 1975 Springer-Verlag Berlin Heidelberg
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Ermol’ev, Y.M., Nurminskiy, E.A. (1975). Limit Extremum Problems. In: Marchuk, G.I. (eds) Optimization Techniques IFIP Technical Conference. Lecture Notes in Computer Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-38527-2_42
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DOI: https://doi.org/10.1007/978-3-662-38527-2_42
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