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Sufficiency and duality in control problems with generalized invexity

Husain I, Ahmed A., Ahmed B.

Journal of Applied Analysis

2008

Vol. 14, nr 1

27-42

Sufficient optimality criteria are derived for a control problem under generalized invexity. A Mond-Weir type dual to the control problem is proposed and various duality theorems are validated under generalized invexity assumptions on functionals appearing in the the problems. It is pointed out that these results can be applied to the control problem with free boundery conditions and have linkage with results for nonlinear programming problems in the presence of inequality and equality constraints already established in the literature.

Sufficiency and duality in multiobjective programming with generalized (F, ρ)-convexity

Ahmad I.

Journal of Applied Analysis

2005

Vol. 11, nr 1

19-33

A multiobjective nonlinear programming problem is considered. Sufficiency theorems are derived for efficient and properly efficient solutions under generalized (F, ρ)-convexity assumptions. Weak, strong and strict converse duality theorems are established for a general Mond-Weir type dual relating properly efficient solutions of the primal and aual problems.