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Fritz John Duality in the Presence of Equality and Inequality Constraints

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Applied Mathematics 2012年第9期3卷 1023-1028页

作者： Iqbal Husain Santosh K. Shrivastav Department of Mathematics Jaypee University of Engineering and Technology Guna India

A dual for a nonlinear programming problem in the presence of equality and inequality constraints which represent many realistic situation, is formulated which uses Fritz John optimality conditions instead of the Karush-Kuhn-Tucker optimality conditions and does not require a constraint qualification. Various duality results, namely, weak, strong, strict-converse and converse duality theorems are established under suitable generalized convexity. A generalized Fritz John type dual to the problem is also formulated and usual duality results are proved. In essence, the duality results do not require any regularity condition if the formulations of dual problems uses Fritz John optimality conditions.

关键词： Second-Order Invexity Second-Order pseudoinvexity Second-Order Quasi-Invexity Nonlinear Programming Fritz John Type Dual

Second-Order Duality for Continuous Programming Containing Support Functions

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Applied Mathematics 2010年第6期1卷 534-541页

作者： Iqbal Husain Mashoob Masoodi 不详

A second-order dual problem is formulated for a class of continuous programming problem in which both objective and constrained functions contain support functions, hence it is nondifferentiable. Under second-order invexity and second-order pseudoinvexity, weak, strong and converse duality theorems are established for this pair of dual problems. Special cases are deduced and a pair of dual continuous problems with natural boundary values is constructed. A close relationship between duality results of our problems and those of the corresponding (static) nonlinear programming problem with support functions is briefly outlined.

关键词： Continuous Programming Second-Order Invexity Second-Order pseudoinvexity Second-Order Duality Nonlinear Programming Support Functions Natural Boundary Values

Multiobjective Duality in Variational Problems with Higher Order Derivatives

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Communications and Network 2010年第2期2卷 138-144页

作者： Iqbal. Husain Rumana. G. Mattoo 不详

A multiobjective variational problem involving higher order derivatives is considered and optimality condi-tions for this problem are derived. A Mond-Weir type dual to this problem is constructed and various duality results are validated under generalized invexity. Some special cases are mentioned and it is also pointed out that our results can be considered as a dynamic generalization of the already existing results in nonlinear programming.

关键词： Multiobjective Variational Problem Efficiency Duality pseudoinvexity Quasinvexity Nonlinear Programming

Optimality Conditions and Second-Order Duality for Nondifferentiable Multiobjective Continuous Programming Problems

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American Journal of Operations Research 2012年第4期2卷 536-545页

作者： I. Husain Vikas K. Jain Department of Mathematics Jaypee University of Engineering and Technology Guna (M.P.) India

Fritz John and Karush-Kuhn-Tucker type optimality conditions for a nondifferentiable multiobjective variational problem are derived. As an application of Karush-Kuhn-Tucker type optimality conditions, Mond-weir type second-order nondifferentiable multiobjective dual variational problems is constructed. Various duality results for the pair of Mond-Weir type second-order dual variational problems are proved under second-order pseudoinvexity and second-order quasi-invexity. A pair of Mond-Weir type dual variational problems with natural boundary values is formulated to derive various duality results. Finally, it is pointed out that our results can be considered as dynamic generalizations of their static counterparts existing in the literature.

关键词： Nondifferentiable Multiobjective Programming Second-Order Invexity Second-Order pseudoinvexity Second-Order Quasi-Invexity Second-Order Duality Nonlinear Multiobjective Programming