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On a Control Problem Containing Support Functions

American Journal of Operations Research 2014年第5期4卷 319-330页

作者： I. Husain A. Ahmed abdul raoof shah Department of Mathematics Jaypee University of Engineering and Technology Guna India Department of Statistics University of Kashmir Srinagar India

A control problem containing support functions in the integrand of the objective of the functional as well as in the inequality constraint function is considered. For this problem, Fritz John and Karush-Kuhn-Tucker type necessary optimality conditions are derived. Using Karush-Kuhn-Tucker type optimality conditions, Wolfe type dual is formulated and usual duality theorems are established under generalized convexity conditions. Special cases are generated. It is also shown that our duality results have linkage with those of nonlinear programming problems involving support functions.

关键词： Control Problem Support Function Optimality Conditions Generalized Convexity Wolfe Type Duality Nonlinear Programming Problem

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On Continuous Programming with Support Functions

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Applied Mathematics 2013年第10期4卷 1441-1449页

作者： Iqbal Husain Santosh K. Shrivastav abdul raoof shah Department of Mathematics Jaypee University of Engineering and Technology Guna India Department of Statistics University of Kashmir Srinagar India

A second-order Mond-Weir type dual problem is formulated for a class of continuous programming problems in which both objective and constraint functions contain support functions;hence it is nondifferentiable. Under second-order strict pseudoinvexity, second-order pseudoinvexity and second-order quasi-invexity assumptions on functionals, weak, strong, strict converse and converse duality theorems are established for this pair of dual continuous programming problems. Special cases are deduced and a pair of dual continuous problems with natural boundary values is constructed. A close relationship between the 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 Generalized Invexity Second-Order Duality Nonlinear Programming Support Functions Natural Boundary Values

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Duality for a Control Problem Involving Support Functions

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Applied Mathematics 2014年第21期5卷 3525-3535页

作者： I. Husain abdul raoof shah Rishi K. Pandey Department of Mathematics Jaypee University of Engineering and Technology Guna India Department of Statistics University of Kashmir Srinagar India

Mond-Weir type duality for control problem with support functions is investigated under generalized convexity conditions. Special cases are derived. A relationship between our results and those of nonlinear programmin... 详细信息

关键词： Control Problem Support Function Generalize Convexity Converse Duality Nonlinear Programming

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