On necessary conditions of optimality in linear spaces
Milan Vlach · Czech digital mathematics library · 1970
Introduction.The approach of the present communication to necessary conditions of optimality is based on the fact that the optimality of an element can be expressed by stating that certain suitable sets have an empty intersection.Therefore, the following scheme is adopted.Let 6 be a set, let CJ be a subset of O and let R be a reflexive and transitive binary relation on G.An element x of Cr will be called optimal with respect to CJ and K -or more briefly (a.).,K)optimal -if (a) x € o , (b) ty € CJ and syRx m& «xR/^ # This scheme is clearly general enough to include both the problems of constrained optimization under scalar* valued criteria and the problemsof constrained optimization under vector-valued criteria.For .x e G let G* mean i^*G: + 0 then X ia not f6) f R>«-©pti-