Multiobjective Variational Problems Involving Higher Order Derivatives


  • B. C. Dash Department of Mathematics, Choudwar College, Choudwar, Cuttack, Odisha, India
  • D. K. Dalai Principal, Govt. Science College, Ayeba, Kendrapara, Odisha, India



Variational Problems, Multiobjective duality, Concavity, Generalized convexity.


In this paper two types of duals are considered for a class of variational problems involving 3rd order derivatives. The duality results are derived without any use of optimality conditions. One set of results is based on Mond weir type dual that has the same objective functional as the primal problem but different constraints. The second set of results is based on a dual of an auxiliary primal with single objective function. Under various convexity and generalized convexity assumptions, duality relationships between primal and its various duals are established. Problems with natural boundary values are considered and the analogs of our results in nonlinear programming are also indicated. Our results are generalizations of those presented by I. Husain, B.Ahmad and Z.Jabeen. 


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How to Cite

Dash, B. C., & Dalai, D. K. (2016). Multiobjective Variational Problems Involving Higher Order Derivatives. International Journal For Research In Mathematics And Statistics, 2(7), 01–20.