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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.

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.

Optimality conditions and duality for multiobjective control problems

Gulati T. R., Husain I., Ahmed A.

Journal of Applied Analysis

2005

Vol. 11, nr 2

225-245

Fritz John and Kuhn-Tucker type necessary optimality conditions for a Pareto optimal (efficient) solution of a multiobjective control problem are obtained by first reducing the multiobjective control problem to a system of single objective control problems, and then using already established optimality conditions. As an application of Kuhn-Tucker type optimality conditions, Wolfe and Mond-Weir type dual multiobjective control problems are formulated and usual duality results are established under invexity / generalized invexity, relating properly efficient solutions of the primal and dual problems. Wolfe and Mond-Weir type dual multiobjective control problems with free boundary conditions are also presented.