Symmetric duality for fractional variational problems with cone constraints

Abstract

Abstract. A pair of symmetric fractional variational programming problems is formulated over cones. Weak, strong, converse and self duality theorems are discussed under pseudoinvexity. Static symmetric dual fractional programs are included as special case and corresponding symmetric duality results are merely stated.

Duality for a class of second order symmetric nondifferentiable fractional variational problems

“…Ahmad et al [2] has taken step in the direction of investigating the duality results for a pair of symmetric fractional variational programming problems over cones and established duality theorems under pseudoinvexity. These results were again extended by Ahmad and Sharma [1] for a pair of multiobjective fractional variational symmetric dual problems over cones.…”

“…a) The problems (PP) and (DP) will reduce to the problem considered by Jayswal and Jha[9], if we take E = F = J = K = {0}. (b) In addition, if A = B = Y = Z = 0, then we will get the problem studied by Ahmad et al[2].…”

Second-order symmetric duality in multiobjective variational problems

“…Mond and Hanson [18] extended symmetric duality to variational problems. Since then, many authors [2,3,4,11,16,19,21] have worked on variational problems. Bector and Husain [6] formulated Wolfe and Mond-Weir type dual variational problems and established various duality results to relate properly ecient solutions of the primal and dual problems.…”