Abstract
Fritz John, and Karush-Kuhn-Tucker type optimality conditions for a constrained variational problem invoving higher order derivatives are obtained. As an application of these Karush-Kuhn-Tucker type optimality conditions, Wolfe and Mond-Weir type duals are formulated, and various duality relationships between the primal problem and each of the duals are established under invexity and generalized invexity. It is also shown that our results can be viewed as dynamic generalizations of those of the mathematical programming already reported in the literature.
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I. Husain is professor in the Department of Mathematics at the National Institute of Technology Srinagar (Formerly Regional Engineering College Srinagar), Kashmir, INDIA. He received his M.A. in mathematics from Banaras Hindu University, Varanasi, INDIA and Ph.D. in Operations Research from Indian Institute of Technology, Delhi. His major areas of research interest are in mathematical programming including continuous time programming, generalization of convexity and optimization (optimality criteria, duality, ect.). He is author and co-author of numerous research papers on previous mentioned research fields. He has refried several research articles. He is a life member of Operational Research Society of India.
Z. Jabeen is lecturer in the Department of Mathematics, National Institute of Technology Srinagar, Kashmir, India. She has obtained M.Sc. in statistics from the University of Kashmir, Srinagr and she is pursuing her Ph.D. programme in operation research under the supervision of Prof. I.Husain.
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Husain, Jabeen, Z. On variational problems involving higher order derivatives. JAMC 17, 433–455 (2005). https://doi.org/10.1007/BF02936067
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DOI: https://doi.org/10.1007/BF02936067