• Title/Summary/Keyword: generalized invexity

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MIXED TYPE DUALITY FOR CONTROL PROBLEMS WITH GENERALIZED INVEXITY

  • Husain, I.;Ahmed, A.;Ahmad, B.
    • Journal of applied mathematics & informatics
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    • v.26 no.5_6
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    • pp.819-837
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    • 2008
  • A mixed type dual to the control problem in order to unify Wolfe and Mond-Weir type dual control problem is presented in various duality results are validated and the generalized invexity assumptions. It is pointed out that our results can be extended to the control problems with free boundary conditions. The duality results for nonlinear programming problems already existing in the literature are deduced as special cases of our results.

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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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OPTIMALITY AND DUALITY FOR NONDIFFERENTIABLE FRACTIONAL PROGRAMMING WITH GENERALIZED INVEXITY

  • Kim, Gwi Soo;Kim, Moon Hee
    • Journal of the Chungcheong Mathematical Society
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    • v.29 no.3
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    • pp.465-475
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    • 2016
  • We establish necessary and sufficient optimality conditions for a class of generalized nondifferentiable fractional optimization programming problems. Moreover, we prove the weak and strong duality theorems under (V, ${\rho}$)-invexity assumption.

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 FOR MULTIOBJECTIVE FRACTIONAL CONTROL PROBLEMS WITH GENERALIZED INVEXITY

  • Nahak, C.;Nanda, S.
    • Journal of applied mathematics & informatics
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    • v.5 no.2
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    • pp.475-488
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    • 1998
  • Wolfe and Mond-Weir type duals for multiobjective con-trol problems are formulated. Under pseudo-invexity/quasi-invexity assumptions of the functions involved, weak and strong duality the-orems are proved to relate efficient solutions of the primal and dual problems.

ON VARIATIONAL PROBLEMS INVOLVING HIGHER ORDER DERIVATIVES

  • HUSAIN I.;JABEEN Z.
    • Journal of applied mathematics & informatics
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    • v.17 no.1_2_3
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    • pp.433-455
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    • 2005
  • Fritz John, and Karush-Kuhn-Tucker type optimality conditions for a constrained variational problem involving higher order derivatives are obtained. As an application of these Karush-Kuhn-Tucker type optimality conditions, Wolfe and Mond-Weir type duals are formulated, and various duality relationships between the primal problem and each of the duals are established under invexity and generalized invexity. It is also shown that our results can be viewed as dynamic generalizations of those of the mathematical programming already reported in the literature.

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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