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Optimality conditions for preinvex functions using symmetric derivative

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Języki publikacji
EN
Abstrakty
EN
As a generalization of convex functions and derivatives, in this paper, the authors study the concept of a symmetric derivative for preinvex functions. Using symmetrical differentiation, they discuss an important characterization for preinvex functions and define symmetrically pseudo-invex and symmetrically quasi-invex functions. They also generalize the first derivative theorem for symmetrically differentiable functions and establish some relationships between symmetrically pseudo-invex and symmetrically quasi-invex functions. They also discuss the Fritz John type optimality conditions for preinvex, symmetrically pseudo-invex and symmetrically quasi-invex functions using symmetrical differentiability.
Rocznik
Strony
91--101
Opis fizyczny
Bibliogr. 23 poz.
Twórcy
  • Department of Mathematics, Hindu College, M.J.P. Rohilkhand University, Bareilly-243003, UP, India
autor
  • Department of Mathematics, Aligarh Muslim University, Aligarh-202002, UP, India
  • Department of Mathematics, Hindu College, M.J.P. Rohilkhand University, Bareilly-243003, UP, India
Bibliografia
  • [1] Aull, C. E. The first symmetric derivative. The American Mathematical Monthly 74, 6 (1967), 708–711.
  • [2] Barani, A., Ghazanfari A, G., and Dragomir S, S. Hermite-Hadamard inequality for functions whose derivatives absolute values are preinvex. Journal of Inequalities and Applications 2012 (2012), 247.
  • [3] Guo, Y., Ye, G., Liu, W., Zhao, D., and Treanţa, S. ˇ On symmetric gH-derivative: Applications to dual interval-valued optimization problems. Chaos, Solitons and Fractals 158 (2022), 112068.
  • [4] Guo, Y., Ye, G., Zhao, D., and Liu, W. gH-symmetrically derivative of interval-valued functions and application in intervalvalued optimization. Symmetry 11 (2019), 1203.
  • [5] Guo, Y., Ye, G., Liu, W., Zhao, D., and Treanţa, S. ˇ Optimality conditions and duality for a class of generalized convex interval-valued optimization problems. Mathematics 9 (2021), 2979.
  • [6] Hanson, M. A. On sufficiency of the Kuhn-Tucker conditions. Journal of Mathematical Analysis and Applications 80, 2 (1981), 545–550.
  • [7] Ho, Q. Necessary and sufficient KKT optimality conditions in non-convex optimization. Optimization Letters 11 (2017), 41–46.
  • [8] Ivanov, V. I. Second-order optimality conditions for inequality constrained problems with locally Lipschitz data. Optimization Letters 4 (2010), 597–608.
  • [9] Larson, L. The symmetric derivative. Transactions of the American Mathematical Society 277 (1983), 589–599.
  • [10] Minch, R. A. Applications of symmetric derivatives in mathematical programming. Mathematical Programming 1, 1 (1971), 307–320.
  • [11] Mishra, S. K. Generalized fractional programming problems containing locally subdifferentiable and ρ-Univex functions. Optimization 41, 2 (1997), 135–158.
  • [12] Mishra, S. K., and Giorgi, G. Invexity and optimization. Springer Science and Business Media, Berlin, 2008.
  • [13] Mishra, S. K., Wang, S. Y., and Lai, K. K. Multiple objective fractional programming involving semi locally type I-preinvex and related functions. Journal of Mathematical Analysis and Applications 310, 2 (2005), 626–640.
  • [14] Mishra, S. K., Wang, S. Y., and Lai, K. K. Optimality and duality for a multi-objective programming problem involving generalized d-type-I and related n-set functions. European Journal of Operational Research 173, 2 (2006), 405–418.
  • [15] Mishra, S. K., Wang, S. Y., and Lai, K. K. On non-smooth α-invex functions and vector variational-like inequality. Optimization Letters 2, 1 (2008), 91–98.
  • [16] Mishra, S. K., Wang, S. Y., and Lai, K. K., and Shi, J. M. Nondifferentiable minimax fractional programming under generalized univexity. Journal of Computational and Applied Mathematics 158, 2 (2003), 379–395.
  • [17] Mohan, S. R., and Neogy, S. K. On invex sets and preinvex functions. Journal of Mathematical Analysis and Applications 189, 3 (1995), 901–908.
  • [18] Sharma, N., Mishra, S. K., and Hamdi, A. A weighted version of Hermite-Hadamard type inequalities for strongly GAconvex functions. International Journal of Advanced and Applied Sciences 7, 3 (2020), 113–118.
  • [19] Sharma, N., Mishra, S. K., and Hamdi, A. Hermite–Hadamard-type inequalities for interval-valued preinvex functions via Riemann–Liouville fractional integrals. Journal of Inequalities and Applications 1 (2021), 98.
  • [20] Thomson, B. S. Symmetric properties of real functions. Dekker, New York, NY, USA, 1994.
  • [21] Weir, T., and Jeyakumar, V. A class of nonconvex functions and mathematical programming. Bulletin of the Australian Mathematical Society 38, 2 (1988), 177–189.
  • [22] Weir, T., and Mond, B. Pre-invex functions in multiobjective optimization. Journal of Mathematical Analysis and Applications 136, 1 (1988), 29–38.
  • [23] Yang, X. Q., and Chen, G.-Y. A class of nonconvex functions and pre-variational inequalities. Journal of Mathematical Analysis and Applications 169, 2 (1992), 359–373.
Uwagi
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-5ba55d79-c740-4a6a-9ad5-9ca41d283968
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