THE STABILITY OF SOLUTION OF SYSTEMS WITH UNDEFINED PARAMETERS OPTIMAL DESIGN PROBLEM

V. I. Levin

Abstract


Our article considers the problem of optimization of incompletely specified functions, namely, functions which parameters are given within range of possible values. It is shown that solution of this problem also requires solving problem of determining stability of optimum of such functions to variation of values of their parameters. A method for obtaining such optimum of incompletely defined functions is presented. Method uses determination of problem. It allows to split original non-deterministic problem into two optimization problem of deterministic functions, which are solved separately. After that solutions are combined into one which is a solution of original problem. The article also provides a method for determining the stability of the optimum found of incompletely defined functions by methods of interval mathematics. We formulate 5 theorems determining the conditions for existence of optimum of incompletely defined function and its resistance to changing the function parameters. Algorithms for verifying the stability function are given

Keywords


system optimization, uncertainty, stability of optimum, variation of parameters, interval mathematics.

References


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DOI: https://doi.org/10.15588/1607-3274-2013-2-11



Copyright (c) 2014 V. I. Levin

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