Characterization of Generalized Invexity in Multiobjective Fractional Variational Problem
AbstractIn 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.
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).
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).