The Journal of the Australian Mathematical Society. Series B. Applied Mathematics

Research Article

On generalised convex mathematical programming

V. Jeyakumara1 and B. Monda2

a1 School of Mathematics, University of New South Wales, Kensington, NSW, Australia 2033.

a2 School of Mathematics and Information Sciences, La Trobe University, Vic. Australia 3083.


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 × X0xs211Dn

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.

(Received February 22 1991)

(Revised March 21 1991)