• Title/Summary/Keyword: invexity

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DUALITY AND SUFFICIENCY IN MULTIOBJECTIVE FRACTIONAL PROGRAMMING WITH INVEXITY

  • Kim, Do-Sang;Lee, Hyo-Jung
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.13 no.2
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    • pp.101-108
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    • 2009
  • In this paper, we introduce generalized multiobjective fractional programming problem with two kinds of inequality constraints. Kuhn-Tucker sufficient and necessary optimality conditions are given. We formulate a generalized multiobjective dual problem and establish weak and strong duality theorems for an efficient solution under generalized convexity conditions.

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GLOBAL PARAMETRIC SUFFICIENT OPTIMALITY CONDITIONS FOR DISCRETE MINMAX FRACTIONAL PROGRAMMING PROBLEMS CONTAINING GENERALIZED $({\theta},\;{\eta},\;{\rho})-V-INVEX$ FUNCTIONS AND ARBITRARY NORMS

  • Zalmai, G.J.
    • Journal of applied mathematics & informatics
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    • v.23 no.1_2
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    • pp.1-23
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    • 2007
  • The purpose of this paper is to develop a fairly large number of sets of global parametric sufficient optimality conditions under various generalized $({\theta},\;{\eta},\;{\rho})-V-invexity$ assumptions for a discrete minmax fractional programming problem involving arbitrary norms.

OPTIMALITY CRITERIA AND DUALITY FOR MULTIOBJECTIVE VARIATIONAL PROBLEMS INVOLVING HIGHER ORDER DERIVATIVES

  • Husain, I.;Ahmed, A.;Rumana, G. Mattoo
    • Journal of applied mathematics & informatics
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    • v.27 no.1_2
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    • pp.123-137
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    • 2009
  • A multiobjective variational problem involving higher order derivatives is considered and Fritz-John and Karush-Kuhn-Tucker type optimality conditions for this problem are derived. As an application of Karush-Kuhn-Tucker optimality conditions, Wolfe type dual to this variational problem is constructed and various duality results are validated under generalized invexity. Some special cases are mentioned and it is also pointed out that our results can be considered as a dynamic generalization of the already existing results in nonlinear programming.

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GENERALIZED INVEXITY AND DUALITY IN MULTIOBJECTIVE NONLINEAR PROGRAMMING

  • Das, Laxminarayan;Nanda, Sudarsan
    • Journal of applied mathematics & informatics
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    • v.11 no.1_2
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    • pp.273-281
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    • 2003
  • The purpose of this paper is to study the duality theorems in cone constrained multiobjective nonlinear programming for pseudo-invex objectives and quasi-invex constrains and the constraint cones are arbitrary closed convex ones and not necessarily the nonnegative orthants.

DUALITY IN MULTIOBJECTIVE FRACTIONAL PROGRAMMING PROBLEMS INVOLVING (Hp, r)-INVEX FUNCTIONS

  • Jayswal, Anurag;Ahmad, I.;Prasad, Ashish Kumar
    • Journal of applied mathematics & informatics
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    • v.32 no.1_2
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    • pp.99-111
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    • 2014
  • In this paper, we have taken step in the direction to establish weak, strong and strict converse duality theorems for three types of dual models related to multiojective fractional programming problems involving ($H_p$, r)-invex functions.

MIXED TYPE MULTIOBJECTIVE VARIATIONAL PROBLEMS WITH HIGHER ORDER DERIVATIVES

  • Husain, I.;Ahmed, A.;Rumana, G. Mattoo
    • Journal of applied mathematics & informatics
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    • v.27 no.1_2
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    • pp.245-257
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    • 2009
  • A mixed type dual for multiobjective variational problem involving higher order derivatives is formulated and various duality results under generalized invexity are established. Special cases are generated and it is also pointed out that our results can be viewed as a dynamic generalization of existing results in the static programming.

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MULTIOBJECTIVE FRACTIONAL PROGRAMMING WITH A MODIFIED OBJECTIVE FUNCTION

  • Kim, Do-Sang
    • Communications of the Korean Mathematical Society
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    • v.20 no.4
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    • pp.837-847
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    • 2005
  • We consider multiobjective fractional programming problems with generalized invexity. An equivalent multiobjective programming problem is formulated by using a modification of the objective function due to Antczak. We give relations between a multiobjective fractional programming problem and an equivalent multiobjective fractional problem which has a modified objective function. And we present modified vector saddle point theorems.