• Title/Summary/Keyword: Continuous programming

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MULTIOBJECTIVE CONTINUOUS PROGRAMMING CONTAINING SUPPORT FUNCTIONS

  • Husain, I.;Ahmed, A.;Rumana, G. Mattoo
    • Journal of applied mathematics & informatics
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    • v.27 no.3_4
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    • pp.603-619
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    • 2009
  • Wolfe and Mond-Weir type dual to a nondifferentiable continuous programming containing support functions are formulated and duality is investigated for these two dual models under invexity and generalized invexity. A close relationship of our duality results with those of nondifferentiable nonlinear programming problem is also pointed out.

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CONTINUOUS PROGRAMMING CONTAINING SUPPORT FUNCTIONS

  • Husain, I.;Jabeen, Z.
    • Journal of applied mathematics & informatics
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    • v.26 no.1_2
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    • pp.75-106
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    • 2008
  • In this paper, we derive necessary optimality conditions for a continuous programming problem in which both objective and constraint functions contain support functions and is, therefore, nondifferentiable. It is shown that under generalized invexity of functionals, Karush-Kuhn-Tucker type optimality conditions for the continuous programming problem are also sufficient. Using these optimality conditions, we construct dual problems of both Wolfe and Mond-Weir types and validate appropriate duality theorems under invexity and generalized invexity. A mixed type dual is also proposed and duality results are validated under generalized invexity. A special case which often occurs in mathematical programming is that in which the support function is the square root of a positive semidefinite quadratic form. Further, it is also pointed out that our results can be considered as dynamic generalizations of those of (static) nonlinear programming with support functions recently incorporated in the literature.

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