Optimality and duality in nonsmooth multiobjective fractional programming problem with constraints
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Tài liệu tham khảo
[1] Aubin JP, Frankowska H (1990) Set-valued analysis. Birkhauser, Boston
[2] Bhurjee AK, Panda G (2015) Multi-objective interval fractional programming problems: an approach for obtaining efficient solutions. OPSEARCH 52:156–167
[3] Bonnans JF, Shapiro A (2000) Perturbation analysis of optimization problems. Springer series in operations research. Springer, New York
[4] Borwein JM (1976) Fractional programming with differentiability. Math Program 11:283–290
[5] Clarke FH (1983) Optimization and nonsmooth analysis. Wiley, New York
[6] Dubey R, Gupta SK, Khan MA (2015) Optimality and duality results for a nondifferentiable multiobjective fractional programming problem. J Inequal Appl 354:1–18. https://doi.org/10.1186/s13660-015-0876-0
[7] Giorgi G, Guerraggio A (1992) On the notion of tangent cone in mathematical programming. Optimization 25:11–23
[8] Gong XH (2008) Optimality conditions for vector equilibrium problems. J Math Anal Appl 342:1455–1466
[9] Gong XH (2010) Scalarization and optimality conditions for vector equilibrium problems. Nonlinear Anal 73:3598–3612
[10] Jahn J, Rauh R (1997) Contingent epiderivatives and set-valued optimization. Math Methods Oper Res 46:193–211
[11] Jiménez B, Novo V (2008) First order optimality conditions in vector optimization involving stable functions. Optimization 57(3):449–471
[12] Jourani A, Thibault L (1993) Approximations and metric regularity in mathematical programming in Banach spaces. Math Oper Res 18:390–401
[13] Khanh PQ, Tung LT (2015) First- and second- order optimality conditions for multiobjective fractional programming. Top 23(2):419–440
[14] Long XJ, Huang YQ, Peng ZY (2011) Optimality conditions for the Henig efficient solution of vector equilibrium problems with constraints. Optim Lett 5:717–728
[15] Luc DT (1989) Theory of vector optimization. In: Lecture notes in economics and mathematical system, vol 319. Springer, Berlin
[16] Luc DT (1991) Contingent derivatives of set-valued maps and applications to vector optimization. Math Program 50:99–111
[17] Luu DV, Su TV (2018) Contingent derivatives and necessary efficiency conditions for vector equilibrium problems with constraints. RAIRO Oper Res 52:543–559
[18] Michel P, Penot JP (1992) A generalized derivative for calm and stable functions. Differ Integr Equ 5(2):433–454
[19] Mishra SK, Jayswal M, An LTM (2012) Duality for nonsmooth semi-infinite programming problems. Optim Lett 6:261–271
[20] Mond M, Weir T (1981) Generallized concavity and duality, generallized concavity in optimization and economics. Academic Press, New York
[21] Osuna-Gómez R, Rufián-Lizana A, Ruíz-Canales P (2000) Multiobjective fractional programming with generalized convexity. Top 8(1):97–110
[22] Pandey Y, Mishra SK (2016) Duality for nonsmooth optimization problems with equilibrium constraints, using convexificators. J Optim Theory Appl 17:694–707
[23] Penot JP (1998a) Optimality conditions for mildly nonsmooth contrained optimization. Optimization 43(4):323–337
[24] Penot JP (1998b) Second-order conditions for optimization problems with constraints. SIAM J Control Optim 37:303–318
[25] Qiu QS (2009) Optimality conditions for vector equilibrium problems with constraints. J Ind Manag Optim 5:783–790
[26] Rockafellar RT (1970) Convex analysis. Princeton University Press, Princeton
[27] Schaible S (1982) Fractional programming. Z Oper Res 27:39–45
[28] Singh C (1981) Optimality conditions in fractional programming. J Optim Theory Appl 33:287–294
[29] Singh C (1986) Nondifferentiable fractional programming with Hanson–Mond classes of functions. J Optim Theory Appl 49:431–447
[30] Su TV (2016) Optimality conditions for vector equilibrium problems in terms of contingent epiderivatives. Numer Funct Anal Optim 37:640–665
[31] Su TV (2017) A new optimality condition for weakly efficient solutions of convex vector equilibrium problems with constraints. J Nonlinear Funct Anal 2017(7):1–14
[32] Su TV (2018) New optimality conditions for unconstrained vector equilibrium problem in terms of contingent derivatives in Banach spaces, 4OR- Q. J Oper Res 16:173–198
[33] Su TV, Dinh DH (2020) Duality results for interval-valued pseudoconvex optimization problem with equilibrium constraints with applications. Comput Appl Math 39(2):127. https://doi.org/10.1007/s40314-020-01153-3
[34] Su TV, Hien ND (2020) Strong Karush–Kuhn–Tucker optimality conditions for weak efficiency in constrained multiobjective programming problems in terms of mordukhovich subdifferentials. Optim Lett. https://doi.org/10.1007/s11590-020-01620-0
[35] Su TV, Luu DV (2020) Higher-order Karush–Kuhn–Tucker optimality conditions for Borwein properly efficient solutions of multiobjective semi-infinite programming. Optimization. https://doi.org/10.1080/02331934.2020.1836633
[36] Tripathy AK (2014) Mixed type duality in multiobjective fractional programming under generalized $$\rho $$-univex function. J Math Model Algorithms Oper Res 13(3):331–340
[37] Tuan ND (2018) On necessary optimality conditions for nonsmooth vector optimization problems with mixed constraints in infinite dimensions. Appl Math Optim 77:515–539
[38] Wolfe P (1961) A duality theorem for nonlinear programming. Q J Appl Math 19:239–244