Abstract
THE discovery of the maximin of functions of many variables is approximated by a problem in which the simultaneous approximation to the solution of both the “external” and also the internal problem is made. The properties of the approximating problem are studied. The theory and various methods of solving maximin problems have already been studied in a number of sources (see, for example, [1–4]). The majority of them give rise to methods in which, at each iteration, it is required to determine one or all the elements yielding a global extremum of the “internal” problem, which in the general case may be a difficult operation. Moreover the extension of these methods to other maximin problems (for example, to a sequential maximin) gives rise to certain difficulties. In this paper the problem of finding the maximin of functions of many variables is approximated by a problem in which a simultaneous approximation to the solution of both the “external”, and also the “internal” problem is made. The properties of the approximating problem are studied. Optimality conditions are given.
Published Version
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