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Articles

Optimality, duality and saddle point analysis for interval-valued nondifferentiable multiobjective fractional programming problems

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Pages 1275-1305 | Received 31 Oct 2019, Accepted 23 Aug 2020, Published online: 17 Sep 2020

References

  • Debdulal G, Ghosh D, Bhuiya SK, et al. A saddle point characterization of efficient solutions for interval optimization problems. J Appl Math Comput. 2018;58:193–217.
  • Osuna-Gómez R, Hernández-Jiménez B, Chalco-Cano Y, et al. New efficiency conditions for multiobjective interval-valued programming problems. Inf Sci. 2017;420:235–248.
  • Singh D, Dar BA, Kim DS. Sufficiency and duality in non-smooth interval valued programming problems. J Ind Manag Optim. 2019;15:647–665.
  • Wu HC. Solving the interval-valued optimization problems based on the concept of null set. J Ind Manag Optim. 2018;14:1157–1178.
  • Zhang J, Liu S, Li L, et al. The KKT optimality conditions in a class of generalized convex optimization problems with an interval valued objective function. Optim Lett. 2014;8:607–631.
  • Wu HC. The Karush-Kuhn-Tucker optimality conditions in an optimization problem with interval-valued objective function. Euro J Oper Res. 2007;176:46–59.
  • Wu HC. The Karush-Kuhn-Tucker optimality conditions in multiobjective programming problems with interval-valued objective functions. Euro J Oper Res. 2009;196:49–60.
  • Zhang J. Optimality condition and wolfe duality for invex interval valued nonlinear programming problems. J Appl Math. 2013;2013, Article ID 641345, 11 pages.
  • Chalco-Cano Y, Lodwick WA, Rufian-Lizana A. Optimality conditions of type KKT for optimization problem with interval valued objective function via generalized derivative. Fuzzy Optim Decis Making. 2013;12:305–322.
  • Singh D, Dar BA, Kim DS. KKT optimality conditions in interval valued multiobjective programming with generalized differentiable functions. Euro J Oper Res. 2016;254:29–39.
  • Li L, Liu S, Zhang J. On fuzzy generalized convex mappings and optimality conditions for fuzzy weakly univex mappings. Fuzzy Sets Systems. 2015;280:107–132.
  • Li L, Zhang J, Zhou C. Optimality conditions for interval-valued univex programming. J Inequal Appl. 2019;1:1–15.
  • Antczak T. Optimality conditions and duality results for nonsmooth vector optimization problems with the multiple interval-valued objective function. Acta Math Sci. 2017;37:1133–1150.
  • Ghosh D. Newton method to obtain efficient solutions of the optimization problems with interval-valued objective functions. J Appl Math Comput. 2017;53:709–731.
  • Ghosh D. A quasi-Newton method with rank-two update to solve interval optimization problems. Int J Appl Comput Math. 2017;3:1719–1738.
  • Sun Y, Wang L. Optimality conditions and duality in nondifferentiable interval-valued programming. J Ind Manage Optim. 2013;9:131–142.
  • Jayswal A, Stancu-Minasian I, Banerjee J. Optimality conditions and duality for interval valued optimization problems using convexifactors. Rend Circ Mat Palermo. 2016;65:17–32.
  • Bhurjee AK, Panda G. Multi-objective interval fractional programming problems: an approach for obtaining efficient solutions. Opsearch. 2015;52:156–167.
  • Bhurjee AK, Panda G. Nonlinear fractional programming problem with inexact paremeter. J Appl Math Informatics. 2013;31:853–867.
  • Effati S, Pakdaman M. Solving the interval-valued linear fractional programming problem. Am J Comput Math. 2012;2:51–55.
  • Hladik M. Generalized linear fractional programming under interval uncertainty. Euro J Oper Res. 2010;205:42–46.
  • Mrinal J, Geetanjali P. Existence of χ-optimal solution of fractional programming problem with interval parameters. J Comput Sci Comput Math. 2015;5:27–32.
  • Pal BB, Moitra BN, Sen S. A linear goal programming approach to multiobjective fractional programming with interval parameter sets. Int J Math Oper Res. 2011;3:697–714.
  • Debnath IP, Gupta SK. Necessary and sufficient optimality conditions for fractional interval-valued optimization problems. In: Decision Science in Action. Singapore: Springer; 2019; p. 155–173.
  • Bazaraa MS, Sherali HD, Shetty CM. Nonlinear programming. New York (NY): Wiley; 1993.
  • Kanniappan P. Necessary conditions for optimality of nondifferentiable convex multiobjective programming. J Optim Theory Appl. 1983;40:167–174.
  • Borwein JM. Fractional programming without differentiability. Math Program. 1976;11:283–290.

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