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Sufficient optimality condition and duality of nondifferentiable minimax ratio constraint problems under (p, r)-ρ-(η, θ)-invexity

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Języki publikacji
EN
Abstrakty
EN
There are several classes of decision-making problems that explicitly or implicitly prompt fractional programming problems. Portfolio selection problems, agricultural planning, information transfer, numerical analysis of stochastic processes, and resource allocation problems are just a few examples. The huge number of applications of minimax fractional programming problems inspired us to work on this topic. This paper is concerned with a nondifferentiable minimax fractional programming problem. We study a parametric dual model, corresponding to the primal problem, and derive the sufficient optimality condition for an optimal solution to the considered problem. Further, we obtain the various duality results under (p, r)-ρ-(η, θ)-invexity assumptions. Also, we identify a function lying exclusively in the class of (−1, 1)-ρ-(η, θ)- invex functions but not in the class of (1,−1)-invex functions and convex function already existing in the literature. We have given a non-trivial model of nondifferentiable minimax problem and obtained its optimal solution using optimality results derived in this paper.
Rocznik
Strony
71--88
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
  • Thapar Institute of Engineering and Technology, Patiala, Punjab 147004, India
autor
  • Thapar Institute of Engineering and Technology, Patiala, Punjab 147004, India
  • Thapar Institute of Engineering and Technology, Patiala, Punjab 147004, India
Bibliografia
  • AHMAD, I. (2003) Optimality conditions and duality in fractional minimax programming involving generalized ρ-invexity. International Journal of Statistics and Systems, 19, 165–180.
  • AHMAD, I., GUPTA, S. K., KAILEY, N., AND AGARWAL, R. P. (2011) Duality in nondifferentiable minimax fractional programming with B-(p, r)-invexity. Journal of Inequalities and Applications, 2011(1), 1–14.
  • AHMAD, I. AND HUSAIN, Z. (2006) Optimality conditions and duality in non-differentiable minimax fractional programming with generalized convexity, Journal of Optimization Theory Applications, 129(2), 255–275.
  • ANTCZAK, T. (2001) (p, r)-invex sets and functions. Journal of Mathematical Analysis and Applications, 263(2), 355–379.
  • ANTCZAK, T., MISHRA, S. K. AND UPADHYAY B. B. (2018) Optimality conditions and duality for generalized fractional minimax programming involving locally Lipschitz (b, ψ,Φ, ρ)-univex functions. Control and Cybernetics, 47(1), 5–32.
  • BOUFI, K. AND ROUBI, A. (2019) Duality results and dual bundle methods based on the dual method of centers for minimax fractional programs. SIAM Journal on Optimization, 29(2), 1578–1602.
  • DU, D. Z. AND PARDALOS P. M. (1995) Minimax and Applications. Kluwer Academic Publishers.
  • DUBEY, R. AND MISHRA, V. N. (2020) Higher-order symmetric duality in non-differentiable multiobjective fractional programming problem over cone contraints. Statistics, Optimization and Information Computing, 8(1), 187–205.
  • FALK, J. E. (1969) Maximization of signal-to-noise ratio in an optical filter. SIAM Journal on Applied Mathematics, 17(3), 582–592.
  • HUSAIN, Z., AHMAD, I. AND SHARMA S. (2009) Second order duality for mini-max fractional programming. Optimization Letter, 3(2), 277–286.
  • JAYSWAL, A. (2008) Non-differentiable minimax fractional programming with generalized a-univexity. Journal of Computational and Applied Mathematics 214(1), 121–135.
  • KHAN, M. A. AND AL-SOLAMY, F. R. (2015) Sufficiency and duality in nondifferentiable minimax fractional programming with (Hp, r)-invexity. Journal of the Egyptian Mathematical Society, 23(1), 208–213.
  • LAI, H. C. AND HUANG, T. Y. (2012) Nondifferentiable minimax fractional programming in complex spaces with parametric duality. Journal of Global Optimization, 53(2), 243–254.
  • LAI, H. C. AND LEE, J. C. (2002) On duality theorems for a nondifferentiable minimax fractional programming. Journal of Computational and Applied Mathematics, 146(1), 115–126.
  • LAI, H. C. AND LIU J. C. (2011) A new characterization on optimality and duality for nondifferentiable minimax fractional programming problems. Journal of Nonlinear and Convex Analysis 12(1), 69–80.
  • LAI, H. C., LIU, J. C. AND TANAKA, K. (1999) Necessary and sufficient conditions for minimax fractional programming. Journal of Mathematical Analysis and Applications, 230(2), 311–328.
  • LONG, J. C. AND QUAN, J. (2011) Optimality conditions and duality for mini-max fractional programming involving nonsmooth generalized univexity. Numerical Algebra, Control and Optimization 1(3), 361–370.
  • LIU, J. C. AND WU, C. S. (1998) On minimax fractional optimality conditions with (F, ρ)-convexity. Journal of Mathematical Analysis and Applications 219(1), 36–51.
  • MANDAL, P. AND NAHAK, C. (2011) Symmetric duality with (p, r)-ρ-(η, θ)-invexity. Applied Mathematics and Computation, 217(21), 8141–8148.
  • SCHMITENDORF, W. E. (1977) Necessary conditions and sufficient optimality conditions for static minmax problems. Journal of Mathematical Analysis and Applications, 57(3), 683–693.
  • SON, T. Q. AND KIM, D. S. (2021) A dual scheme for solving linear countable semi-infinite fractional programming problems. Optimization Letters, 1–14.
  • SONALI, S., SHARMA, V. AND KAILEY, N. (2020) Higher-order non-symmetric duality for nondifferentiable minimax fractional programs with square root terms. Acta Mathematica Scientia, 40(1), 127–140.
  • TANIMOTO, S. (1981) Duality for a class of nondifferentiable mathematical programming problems. Journal of Mathematical Analysis and Applications, 79(2), 283–294.
  • ZHENG, X. J. AND CHENG, L. (2007) Minimax fractional programming under nonsmooth generalized (F, ρ, θ)-d-univex. Journal of Mathematical Analysis and Applications, 328(1), 676–689.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-016604ef-ee90-4a71-ae4a-d939629d7e69
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