International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 6, Pages 371-383
doi:10.1155/S0161171201005476

Optimization problems for set functions

Abstract

This paper gives the formal definition of a class of optimization problems, that is, problems of finding conditional extrema of given set-measurable functions. It also formulates the generalization of Lyapunov convexity theorem which is used in the proof of first-order optimality conditions for the mentioned class of optimization problems.