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.
Journal
of Ravishankar University Vol. 4-5
No B (Science) 1991-92 pp.157-167
ISSN 0970 5910
Necessary optimality criteria on a Banach space
D.K.
Bhattacharya and S. Bandyopadhyay
Department
of Pure Mathematics, University of
Calcutta.
Ms.: Received 9-11-89 Revised 31-8-91
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.
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