Abasov, T. M. Normal sets and monotonic functions and their applications. (English. Russian original) Zbl 0799.90102 Comput. Math. Math. Phys. 33, No. 7, 885-890 (1993); translation from Zh. Vychisl. Mat. Mat. Fiz. 33, No. 7, 1004-1011 (1993). Summary: Analogues of the separability theorems for normal and \(\mathbb{R}^ n_ +\)- stable sets are proved and some results for monotonic functions are obtained using them. In particular, it is shown that monotonic functions can be represented in the form of a supremum or infimum of a certain family of functions, and necessary and sufficient conditions for an extremum are obtained. Cited in 1 Document MSC: 90C29 Multi-objective and goal programming Keywords:separability theorems; monotonic functions PDF BibTeX XML Cite \textit{T. M. Abasov}, Comput. Math. Math. Phys. 33, No. 7, 1004--1011 (1993; Zbl 0799.90102); translation from Zh. Vychisl. Mat. Mat. Fiz. 33, No. 7, 1004--1011 (1993) OpenURL