Open Access
Issue
RAIRO-Oper. Res.
Volume 59, Number 5, September-October 2025
Page(s) 3403 - 3421
DOI https://doi.org/10.1051/ro/2025130
Published online 04 November 2025
  • T. Antczak and A. Pitea, Parametric approach to multitime multiobjective fractional variational problems under (f, ρ)-convexity. Opt. Control App. Methods 37 (2016) 831–847. [CrossRef] [Google Scholar]
  • C.R. Bector and I. Husain, Duality for multiobjective variational problems. J. Math. Anal. App. 166 (1992) 214–229. [Google Scholar]
  • X. Chen, Second-order duality for the variational problems. J. Math. Anal. App. 286 (2003) 261–270. [Google Scholar]
  • G. Dantzig, E. Eisenberg and R.W. Cottle, Symmetric dual nonlinear programs. Pac. J. Math. 15 (1965) 809–812. [CrossRef] [Google Scholar]
  • V. Dhingra and N. Kailey, Optimality and duality for second-order interval-valued variational problems. J. Appl. Math. Comput. 68 (2022) 3147–3162. [Google Scholar]
  • W.S. Dorn, A symmetric dual theorem for quadratic programs. J. Oper. Res. Soc. Jpn. 2 (1960) 93–97. [Google Scholar]
  • V.P. Dubey, D. Kumar, H.M. Alshehri, J. Singh and D. Baleanu, Generalized invexity and duality in multiobjective variational problems involving non-singular fractional derivative. Open Phys. 20 (2022) 939–962. [Google Scholar]
  • T.R. Gulati and G. Mehndiratta, Optimality and duality for second-order multiobjective variational problems. Eur. J. Pure Appl. Math. 3 (2010) 786–805. [MathSciNet] [Google Scholar]
  • T. Gulati, I. Husain and A. Ahmed, Symmetric duality for multiobjective variational problems. J. Math. Anal. App. 210 (1997) 22–38. [Google Scholar]
  • M.A. Hanson, Bounds for functionally convex optimal control problems. J. Math. Anal. App. 8 (1964) 84–89. [Google Scholar]
  • I. Husain, A. Ahmed and M. Masoodi, Second-order duality for variational problems. Eur. J. Pure Appl. Math. 2 (2009) 278–295. [Google Scholar]
  • A. Jayswal and S. Jha, Second order symmetric duality in fractional variational problems over cone constraints. Yugoslav J. Oper. Res. 28 (2018) 39–57. [Google Scholar]
  • A. Jayswal, I. Stancu-Minasian and S. Choudhury, Second order duality for variational problems involving generalized convexity. Opsearch 52 (2015) 582–596. [CrossRef] [MathSciNet] [Google Scholar]
  • A. Jayswal, S. Jha, A.K. Prasad and I. Ahmad, Second-order symmetric duality in variational control problems over cone constraints. Asia-Pac. J. Oper. Res. 35 (2018) 1850028. [Google Scholar]
  • N. Kailey and S.K. Gupta, Duality for a class of symmetric nondifferentiable multiobjective fractional variational problems with generalized (F, α, ρ, d)-convexity. Math. Comput. Model. 57 (2013) 1453–1465. [Google Scholar]
  • A. Kaur, M.K. Sharma and I. Ahmad, Multiobjective symmetric duality in higher-order fractional variational programming. Asia-Pac. J. Oper. Res. 40 (2023) 2250008. [Google Scholar]
  • D.S. Kim and G.M. Lee, Symmetric duality with pseudo-invexity in variational problems. Optimization 28 (1993) 9–16. [Google Scholar]
  • R. Kumar, V.N. Mishra and R. Dubey, Non-differentiable second-order symmetric multiobjective fractional variational programming with cones constraints. RAIRO-Oper. Res. 58 (2024) 4553–4574. [Google Scholar]
  • S.K. Mishra and R.N. Mukherjee, Duality for multiobjective fractional variational problems. J. Math. Anal. App. 186 (1994) 711–725. [Google Scholar]
  • S.K. Mishra, S.Y. Wang and K.K. Lai, Symmetric duality for a class of nondifferentiable multi-objective fractional variational problems. J. Math. Anal. App. 333 (2007) 1093–1110. [Google Scholar]
  • Ş. Mititelu and I.M. Stancu-Minasian, Efficiency and duality for multiobjective fractional variational problems with (ρ, b)-quasiinvexity. Yugoslav J. Oper. Res. 19 (2009) 85–99. [Google Scholar]
  • B. Mond and M.A. Hanson, Duality for variational problems. J. Math. Anal. App. 18 (1967) 355–364. [Google Scholar]
  • B. Mond and M.A. Hanson, Symmetric duality for variational problems. J. Math. Anal. App. 23 (1968) 161–172. [Google Scholar]
  • B. Mond and T. Weir, Generalized concavity and duality, in Generalized Concavity in Optimization and Economics, edited by S. Schaible and W.T. Ziemba. Academic Press, New York (1981) 263–279. [Google Scholar]
  • S. Padhan and C. Nahak, Second order duality for the variational problems under ρ − (η, θ)-invexity. Comput. Math. App. 60 (2010) 3072–3081. [Google Scholar]
  • S. Padhan and C. Nahak, Higher-order generalized invexity in variational problems. Math. Methods Appl. Sci. 36 (2013) 1334–1341. [Google Scholar]
  • S.K. Padhan, P.K. Behera and R.N. Mohapatra, Second-order symmetric duality andvariational problems, in Mathematics and Computing, edited by R.N. Mohapatra, D.R. Chowdhury and D. Giri. Springer India, New Delhi (2015) 49–57. [Google Scholar]
  • N. Pokharna and I.P. Tripathi, e-optimality and e-duality results for multiobjective variational problems and application to the cake-eating problem. J. Ind. Manage. Opt. 20 (2024) 1867–1896. [Google Scholar]
  • A.K. Prasad, A.P. Singh and S. Khatri, Duality for a class of second order symmetric nondifferentiable fractional variational problems. Yugoslav J. Oper. Res. 30 (2020) 121–136. [Google Scholar]
  • G. Sachdev, K. Verma and T.R. Gulati, Second-order symmetric duality in multiobjective variational problems. Yugoslav J. Oper. Res. 29 (2019) 295–308. [Google Scholar]
  • V. Singh, I. Ahmad, S.K. Gupta and S. Al-Homidan, Duality for multiobjective variational problems under second-order (ø, ρ)-invexity. Filomat 35 (2021) 605–615. [Google Scholar]
  • I. Smart and B. Mond, Symmetric duality with invexity in variational problems. J. Math. Anal. App. 152 (1990) 536–545. [Google Scholar]
  • S.K. Suneja, S. Aggarwal and S. Davar, Multiobjective symmetric duality involving cones. Eur. J. Oper. Res. 141 (2002) 471–479. [Google Scholar]
  • B.B. Upadhyay, A. Ghosh, P. Mishra and S. Treant¸ă, Optimality conditions and duality for multiobjective semi-infinite programming problems on hadamard manifolds using generalized geodesic convexity. RAIRO-Oper. Res. 56 (2022) 2037–2065. [Google Scholar]

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