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Duality for a Non‐Convex Program in a Real Banach Space
Author(s) -
Bector C. R.,
Bhatt S. K.
Publication year - 1977
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19770570311
Subject(s) - duality (order theory) , mathematics , convex analysis , fenchel's duality theorem , perturbation function , banach space , danskin's theorem , pure mathematics , subderivative , convex set , reflexive space , brouwer fixed point theorem , regular polygon , convex optimization , fixed point theorem , interpolation space , geometry , functional analysis , biochemistry , chemistry , gene
This paper works out a direct duality theorem for a mathematical program in Banach space having ratio of a convex and a linear functional as its objective function. For a convex program in real BANACH space, RITTER [1] extended the WOLFE 's duality theorem for a convex program in EUCLIDEAN space. It however turns out that WOLFE 's direct duality theorem does not hold for a pseudoconvex program in general [2, p. 158]. BECTOR [3] succeeded in proving WOLFE 's direct duality theorem for a mathematical program in EUCLIDEAN space in which the pseudo‐convex objective function is the ratio of a convex and a linear function. The present paper aims at extending this result for programs in BANACH space. The approach to establish the direct duality theorem, however, is the same as that of RITTER , i.e. using the weak duality theorem and the Kuhn‐Tucker necessary conditions for optimality.