Extremum conditions in terms of adjoint exhausters

Notion of exhauster proposed by V. F. Demyanov and A. M. Rubinov played important role in evolution of nonsmooth analysis. This tool showed it’s effectiveness in solving nondifferentable optimization problems. The necessary minimum conditions are formulated in terms of an upper exhauster and the necessary maximum conditions are formulated in terms of a lower exhauster. Later the problem of finding minimum conditions in terms of the lower exhauster and maximum conditions in terms of the upper exhauster was solved by V. A. Roshchina. As further development of Demyanov’s and Roshchina’s ideas an attempt to formulate this conditions in another way was undertaken.