• Title/Summary/Keyword: Wolfe type second order dual

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NONDIFFERENTIABLE SECOND ORDER SELF AND SYMMETRIC DUAL MULTIOBJECTIVE PROGRAMS

  • Husain, I.;Ahmed, A.;Masoodi, Mashoob
    • Journal of applied mathematics & informatics
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    • v.26 no.3_4
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    • pp.549-561
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    • 2008
  • In this paper, we construct a pair of Wolfe type second order symmetric dual problems, in which each component of the objective function contains support function and is, therefore, nondifferentiable. For this problem, we validate weak, strong and converse duality theorems under bonvexity - boncavity assumptions. A second order self duality theorem is also proved under additional appropriate conditions.

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NONDIFFERENTIABLE SECOND-ORDER MINIMAX MIXED INTEGER SYMMETRIC DUALITY

  • Gulati, Tilak Raj;Gupta, Shiv Kumar
    • Journal of the Korean Mathematical Society
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    • v.48 no.1
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    • pp.13-21
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    • 2011
  • In this paper, a pair of Wolfe type nondifferentiable sec-ond order symmetric minimax mixed integer dual problems is formu-lated. Symmetric and self-duality theorems are established under $\eta_1$-bonvexity/$\eta_2$-boncavity assumptions. Several known results are obtained as special cases. Examples of such primal and dual problems are also given.

MULTIOBJECTIVE SECOND-ORDER NONDIFFERENTIABLE SYMMETRIC DUALITY INVOLVING (F, $\alpha$, $\rho$, d)-CONVEX FUNCTIONS

  • Gupta, S.K.;Kailey, N.;Sharma, M.K.
    • Journal of applied mathematics & informatics
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    • v.28 no.5_6
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    • pp.1395-1408
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    • 2010
  • In this paper, a pair of Wolfe type second-order nondifferentiable multiobjective symmetric dual program over arbitrary cones is formulated. Weak, strong and converse duality theorems are established under second-order (F, $\alpha$, $\rho$, d)-convexity assumptions. An illustration is given to show that second-order (F, $\alpha$, $\rho$, d)-convex functions are generalization of second-order F-convex functions. Several known results including many recent works are obtained as special cases.