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On Second-Order Duality in Nondifferentiable Continuous Programming

American Journal of Operations Research 2012年第3期2卷 289-295页

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

A Mond-Weir type second-order dual continuous programming problem associated with a class of nondifferentiable continuous programming problems is formulated. Under second-order pseudo-invexity and second-order quasi-invexity various duality theorems are established for this pair of dual continuous programming problems. A pair of dual continuous programming problems with natural boundary values is constructed and the proofs of its various duality results are briefly outlined. Further, it is shown that our results can be regarded as dynamic generalizations of corresponding (static) second-order duality theorems for a class of nondifferentiable nonlinear programming problems already studied in the literature.

关键词： Continuous Programming Second-Order invexity Second-Order Pseudoinvexity Second-Order quasi-invexity Second-Order Duality Nonlinear Programming

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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

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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

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