## 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.

### MSC:

 90C29 Multi-objective and goal programming

### Keywords:

separability theorems; monotonic functions