Applied mathematics

Extremum conditions in terms of generalized adjoint exhausters

M. E. Abbasov

St. Petersburg State University, St. Petersburg 199034, Russian Federation

Abstract: The notion of exhauster from the works of B. N. Pshenichny, V. F. Demyanov, A. M. Rubinov devoted to the study of nonconvex functions. By means of these tools one can describe the optimality conditions, build the direction of descent and ascent. The introduction of generalized exhausters allowed to expand the class of functions under consideration. In the present work an attempts is made to get the minimum conditions in terms of generalized lower exhausters and conditions of the maximum in terms of generalized upper exhausters. The results are illustrated by examples. Bibliogr. 11.

Keywords: nonsmooth analysis, nondifferentiable optimization, adjoint generalized exhauster, extremum, strict extremum, necessary and sufficient conditions.

UDC: 519.3+519.7

Received: March 21, 2013