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(F, ρ)-invexity of higher order for multiobjective fractional variational problem

Kumar P., Sharma B.

Control and Cybernetics

2018

Vol. 47, no. 2

131--146

Multiobjective fractional variational problem is considered and suﬃcient optimality conditions, characterizing eﬃciency of higher order, are obtained under the assumptions of (F,ρ)−invexity of higher order on the functionals involved. Parametric higher order dual of the above stated problem is proposed. Duality theorems are proved to relate eﬃcient solutions of higher order for primal and its dual problem using generalized class of functionals.

On multiobjective nonlinear programming with support functions

Husain I., Ahmed A., Mattoo R. G.

Journal of Applied Analysis

2010

Vol. 16, nr 2

171-187

A multiobjective programming problem containing support functions is considered. Wolfe and Mond-Weir type vector duals to this problem are constructed and various duality results are validated under invexity and generalized invexity assumptions. Special cases are generated from these results.

A remark on problems with nonnegative variable in mathematical programming

Galewski Marek

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

2002

z. 26 [199]

67-76

We provide sufficient conditions involving invexity to the nonlinear programming problem with nonnegative variable and both inequality and equality constriants. We also consider the Mond-Wiers duals to such a problem.

On some connection between invex and convex problems in nonlinear programming

Galewski M.

Control and Cybernetics

2001

Vol. 30, no 1

11-22

A method of solving problems involving invex functions via certain convex problems is presented. Nonsmooth problems are also considered. A definition of such a Fenchel-Young type duality for an invex function f that its second dual is equal to f is provided.