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On generalised convex mathematical programming

Published online by Cambridge University Press:  17 February 2009

V. Jeyakumar  and
B. Mond
V. Jeyakumar
Affiliation:
School of Mathematics, University of New South Wales, Kensington, NSW, Australia2033.
B. Mond
Affiliation:
School of Mathematics and Information Sciences, La Trobe University, Vic.Australia3083.
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Abstract

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The sufficient optimality conditions and duality results have recently been given for the following generalised convex programming problem:

where the funtion f and g satisfy

for some η: X0 × X0 → ℝn

It is shown here that a relaxation defining the above generalised convexity leads to a new class of multi-objective problems which preserves the sufficient optimality and duality results in the scalar case, and avoids the major difficulty of verifying that the inequality holds for the same function η(. , .). Further, this relaxation allows one to treat certain nonlinear multi-objective fractional programming problems and some other classes of nonlinear (composite) problems as special cases.

Type
Research Article
Information
The ANZIAM Journal , Volume 34 , Issue 1 , July 1992 , pp. 43 - 53
Copyright
Copyright © Australian Mathematical Society 1992

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