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Author(s): D.K. Bhattacharya, S. Bandyopadhyay

Email(s): Email ID Not Available

Address: Department of Pure Mathematics, University of Calcutta

Published In:   Volume - 4,      Issue - 1,     Year - 1991


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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