ABSTRACT:
Let X be a real Banach space and let x• be its dual space. Let f : X -R and g: X - Rm be Frechtt differentiable functions defined on an open set X o C X. Let the maximizing problem be as follows; To find XE:X' such that f(X) < f(x), Vx < X' Where XE:X'- { X-:XE>X0 g(x) > 0 }. The object of this paper is to deduce first Fritz - John type of necessary conditions for the above maximizing problem with 1he help of s1rict separation theorem for closed convex cones in Banach space and them Kuhn·Tucker types of necessary conditions under suitable constraint qualifications.
Cite this article:
Bhattacharya and Bandyopadhyay (1991). Necessary optimality criteria on a Banach space. Journal of Ravishankar University (Part-B: Science), 4(1), pp.157-167.