ON NONSMOOTH PROBLEMS OF MATHEMATICAL PROGRAMMING

This paper derives necessary first and second-order extremum conditions for nonsmooth extremal problems with constraints in a Fréchet space. It also derives an analog of the Kuhn-Tucker theorem for a mathematical programming problem in a Fréchet space in the case of an operator constraint with equality. It also derives a second-order necessary extremum condition for nonsmooth mathematical programming problems, which is an analog of the second-order Levitin-Milyutin-Osmolovskii theorem.