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

  • Gupta, S.K. (Department of Mathematics, Indian Institute of Technology Patna) ;
  • Kailey, N. (School of Mathematics and Computer Applications, Thapar University) ;
  • Sharma, M.K. (School of Mathematics and Computer Applications, Thapar University)
  • Received : 2010.01.24
  • Accepted : 2010.05.15
  • Published : 2010.09.30

Abstract

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.

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