Characterization of Generalized Invexity in Multiobjective Fractional Variational Problem

  • Promila Kumar
  • Jyoti Dagar
  • Bharti Sharma
Keywords: Multiobjective, Fractional, Vari- ational Problem, Pseudoinvexity, Ecient Solution, F-Fritz John Point, F-Kuhn-Tucker Point.

Abstract

In this article we define certain conditions on the functionals of multi-objective fractional variational problem in order that it becomes F-Kuhn Tucker pseudo invex or F-Fritz John pseudo invex. We also define F-KT and F-FJ points. Further, these problems are characterized such that all F-KT and F-FJ points become efficient solutions for the featured problem. An example is presented to verify the existence of F-KT point. A Parametric dual is proposed and various duality results are proved under the assumption of F-KT as well as F-FJ pseudo invexity.

References

B. Mond, and M. A. Hanson, Duality for variational problem, Journal of Mathematical Analysis and Applications, vol. 18, pp. 355–364, (1967).

B. Mond, and I. Smart, Duality and sufficiency in control problems with invexity, Journal of Mathematical Analysis and Applications, vol. 136, pp. 325–333 (1988) .

C. R. Bector, S. Chandra, and I. Husain, Optimality condition and sub-differentiable multi-objective fractional programming, Journal of Optimization theory and Applications, vol. 79, pp.105–125, (1988) .

D. Bhatia, and P. Kumar, Multi-objective control problem with generalized invexity, Journal of Mathematical Analysis and Applications, vol. 189, pp.676–692, (1995).

D. Bhatia, and P. Kumar, On multi-objective fractional control problems, Journal of Operational Research, vol. 13, pp.115–132, (1996).

D. Bhatia, and P. Kumar, Duality for variational problems with b-vex functions, Optimization, vol. 36, pp.347–360, (1996).

D. H. Martin, The essence of invexity, Journal of Optimization Theory and Applications, vol. 47, pp. 65–76, (1985).

I. M. Gelfand, and S. V. Fomin, Calculas of Variation, Prentice hall, Inc. Englewood Cliff, New Jersy pp. 34-35, (1963).

M. Arana, R. Osuna, G. Ruiz, and M. Rojas, On variational problems: Characterization of solutions and duality, Journal of Mathematical Analysis and Applications, vol. 311, pp. 1–12, (2005).

M. Arana, A. Rufian, R. Osuna, and G. Ruiz, Pseudoinvexity, optimality conditions and efficiency in multi-objective problems; duality, Nonlinear Analysis, vol. 68, pp. 24–34, (2008).

M. Arana, G. Ruiz,A. Rufian, and R. Osuna, Weak efficiency in multi-objective variational problems under generalized convexity, Journal Of Global Optimization, vol. 52, pp. 109–121, (2012).

M. A. Hanson, On Sufficiency of Kuhn Tucker conditions, Journal of Mathematical Analysis and Applications vol. 80, pp.545-550, (1981).

M. A. Hanson, Bounds for functionally convex optimal control problems, Journal of Mathematical Analysis and Applications,vol. 8, pp.84–89,(1964).

M. A. Jimenez, G. R. Garzon, A. R. Lizana, and R. O. Gomez, A necessary and sufficient condition for duality in multi-objective variational problems, European Journal of Operational Research, vol. 201, pp.672–681,(2010).

P. Kumar, and Jyoti, Generalized invexity of higher order and its applications in variational problems, Applied Mathematics, vol. 6, No. 9, pp.1638–1648, (2015).

P. Kumar, and B. Sharma,Weak efficiency of higher order for multi-objective fractional variational problems, Opsearch, vol. 53,, No. 3, pp.538–552, (2016).

R. Patel, Mixed type duality for multi-objective fractional variational problems using (b; F; ) convexity, Journal of Combinatorics,Information ans System Sciences, vol. 35, No. 1/2, pp.59–79, (2010).

S.K.Mishra, and R.N.Mukherjee, Duality for multi-objective fractional variational problems, Journal of Mathematical Analysis and Applications,vol. 186, pp.711–725, (1994).

S. Mititelu, and I.M.Stancu-Minasian, Efficiency and duality for multi-objective fractional variational problems with (; b) quasiinvexity, Yogoslav Journal of Operations Research, vol. 19, pp.85–99, (2009).

Published
2016-12-07
How to Cite
Kumar, P., Dagar, J., & Sharma, B. (2016). Characterization of Generalized Invexity in Multiobjective Fractional Variational Problem. Statistics, Optimization & Information Computing, 4(4), 342-349. https://doi.org/10.19139/soic.v4i4.208
Section
Research Articles