Necessary and Sufficient Conditions for a Local Minimum. 2: Conditions of Levitin–Miljutin–Osmolovskii Type

The general approach suggested in the preceding paper with the same title is applied to derive various necessary conditions similar to those which have been recently found by Levitin, Miljutin and Osmolovskii. The main technical tool is a new kind of approximation extending those used by the three authors. Normal problems are separately considered; conditions which are both necessary and sufficient are established for such problems.