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    ×
  • The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, Volume 34, Issue 1
  • July 1992, pp. 43-53

On generalised convex mathematical programming

  • V. Jeyakumar (a1) and B. Mond (a2)
  • DOI: http://dx.doi.org/10.1017/S0334270000007372
  • Published online: 01 February 2009
Abstract
Abstract

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.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[3] K. L. Chew and E. U. Choo , “Pseudolinearity and efficiency”, Mathematical Programming 28 (1984) 226239.

[7] B. D. Craven , Mathematical programming and control theory, (Chapman and Hall, London, 1978).

[9] M. A. Hanson , “On sufficiency of the Kuhn-Tucker conditions”, J. Math. Anal. Appl. 80 (1981) 544550.

[10] D. H. Martin , “The essence of invexity”, J. Optim. Theore. Appl. 47 (1985) 6576.

[13] T. Weir , B. Mond and B. D. Craven , “On duality for weakly minimized vector valued optimisation problems”, Optimisation 17 (1986) 711721.

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