Higher-order symmetric duality in nondifferentiable multiobjective fractional programming problem over cone contraints
AbstractIn this paper, we introduce the definition of higher-order K-(C, α, ρ, d)-convexity/pseudoconvexity over cone and discuss a nontrivial numerical examples for existing such type of functions. The purpose of the paper is to study higher order fractional symmetric duality over arbitrary cones for nondifferentiable Mond-Weir type programs under higher- order K-(C, α, ρ, d)-convexity/pseudoconvexity assumptions. Next, we prove appropriate duality relations under aforesaid assumptions.
O.L. Mangasarian, Second-and higher-order duality in nonlinear programming, Journal of Mathematical Analysis and Applications,vol. 51, no. 1, 607-620, 1975.
X.H. Chen, Higher-order symmetric duality in nondifferentiable multiobjective programming problems, Journal of MathematicalAnalysis and Applications, vol. 290, no.12, pp. 423-435, 2004.
Mohamed Abd El-Hady Kassem, Higher-order symmetric duality in vector optimization problem involving generalized cone-invex functions, Appl. Math. Comput., vol. 2, no. 2, pp. 405-409, 2009.
S.K. Suneja, M.K. Srivastava and M. Bhatia, Duality in Multiobjective Fractional Programming with Support Functions, Journal of Mathematical Analysis and Application., vol. 347, no. 1, pp. 8-17, 2008.
G. Ying, Higher-order symmetric duality for a class of multiobjective fractional programming problems, Journal of Inequalities and Applications, 142, doi.org/10.1186/1029-242X-2012-142, 2012.
R. Dubey and S.K. Gupta, Duality for a nondifferentiable multiobjective higher-order symmetric fractional programming problem with cone constraints, Journal of Nonlinear Analysis and Optimization, Vol.7, no.1, 1-15, 2016.
B.D. Craven, Lagrange conditions and quasiduality, Bulletin of the Australian Mathematical Society, vol. 16, no.3, pp.325-339,1977.
S.K. Gupta and N. Kailey, Second-order multiobjective symmetric duality involving cone-bonvex functions, Journal of Global Optimization,vol. 55, no.1, pp.125-140, 2013.
S.K. Gupta, N. Kailey and M.K. Sharma, Multiobjective second-order nondifferentiable symmetric duality involving (F;α ;ρ; d)-convex function, Journal of applied mathematics and information sciences, vol.28, pp. 1395-1408, 2010.
X.J. Long, Optimality conditions and duality for nondifferentiable multiobjective fractional programming problems with(C, α, ρ, d)-convexity, Journal of Optimization Theory and Applications, vol.148, no. 1, pp. 197-208, 2011.
R. Dubey, S.K. Gupta and M.A. Khan, Optimality and duality results for a nondifferentiable multiobjective fractional programming problem, Journal of Inequalities and Applications, vol.354, DOI 10.1186/s13660-015-0876-0, 2015.
R. Dubey and S.K. Gupta, Duality for a nondifferentiable multiobjective higher-order symmetric fractional programming problems with cone constraints, Journal of Nonlinear Analysis and Applications, vol.7 , pp.1-15, pp. 294-311, DOI: 10.4236/ajor.2018.84017,2016.
Vandana, R. Dubey, Deepmala, L.N. Mishra and V.N. Mishra, Duality relations for a class of a multiobjective fractional
programming problem involving support functions, American Journal of Operations Research, vol. 8 , pp. 294-311, DOI:
R. Dubey, Vandana and V.N. Mishra, Second order multiobjective symmetric programming problem and duality relations under (F;Gf )-convexity, Global Journal of Engineering Science and Researches, vol. 5, no. 8, pp.187-199, DOI: 10.5281/zenodo.1341853,2018.
R. Dubey, V.N. Mishra and P. Tomar, Duality relations for second-order programming problem under (G; f )-bonvexity assumptions,Asian-European Journal of Mathematics, vol.13 , no. 1, pp.1-17, DOI: 10.1142/S1793557120500448, 2020.
- 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).