Optimality conditions and duality in terms of convexificators for multiobjective bilevel programming problem with equilibrium constraints
Tác giả
Tài liệu tham khảo
[1] Babahadda H, Gadhi N (2006) Necessary optimality conditions for bilevel optimization problems using convexificators. J Glob Optim 34:535–549
[2] Ben-Ayed O, Blair CE (1990) Computational difficulties of bilevel linear programming. Oper Res 38:556–560
[3] Bot RI, Grad S-M (2010) Wolfe duality and Mond–Weir duality via perturbations. Nonlinear Anal Theory Methods Appl 73(2):374–384
[4] Clarke FH (1983) Optimization and nonsmooth analysis. Wiley, New York
[5] Colson B, Marcotte P, Savard G (2007) An overview of bilevel programming. Ann Oper Res 153:235–256
[6] Chuong TD (2018) Optimality conditions for nonsmooth multiobjective bilevel optimization problems. Ann Oper Res (Online). https://doi.org/10.1007/s10479-017-2734-6
[7] Dempe S (1992) A necessary and sufficient optimality condition for bilevel programming problem. Optim 25:341–354
[8] Dempe S (2002) Foundation of bilevel programming. Kluwer Academic Publishers, Dordrecht
[9] Dempe S, Pilecka M (2015) Necessary optimality conditions for optimistic bilevel programming problems using set-valued programming. J Glob Optim 61:769–788
[10] Dempe S, Zemkoho AB (2012) Bilevel road pricing: theoretical analysis and optimality conditions. Ann Oper Res 196:223–240
[11] Dempe S, Gadhi N, Zemkoho AB (2013) New optimality conditions for the semivectorial bilevel optimization problem. J Optim Theory Appl 147:54–74
[12] Dempe S, Gadhi N, Idrissi MEL (2020) Optimality conditions in terms of convexificators for a bilevel multiobjective optimization problem. Optim. https://doi.org/10.1080/02331934.2020.1750610
[13] Dutta J, Chandra S (2004) Convexificators, generalized convexity and vector optimization. Optim. 53:77–94
[14] Eichfelder G (2010) Multiobjective bilevel optimization. Math Program Ser A 123:419–449
[15] Ehrgott M (2005) Multicriteria optimization. Springer, Berlin
[16] Jahn J (2004) Vector optimization. Theory, applications, and extensions. Springer, Berlin
[17] Jeyakumar V, Luc DT (1999) Nonsmooth calculus, minimality, and monotonicity of convexificators. J Optim Theory Appl 101:599–621
[18] Gadhi N, Dempe S (2013) Necessary optimality conditions and a new approach to multiobjective bilevel optimization problems. J Optim Theory Appl. https://doi.org/10.1007/s10957-012-0046-1
[19] Gong XH (2010) Scalarization and optimality conditions for vector equilibrium problems. Nonlinear Anal 73:3598–3612
[20] Hiriart-Urruty JB (1979) Tangent cones, generalized gradients and mathematical programming in Banach spaces. Math Oper Res 4:79–97
[21] Hiriart-Urruty JB, Lemaréchal C (1993) Convex analysis and minimization algorithms I. Springer, Berlin
[22] Li XF, Zhang JZ (2006) Necessary optimality conditions in terms of convexificators in Lipschitz optimization. J Optim Theory Appl 131:429–452
[23] Luo ZQ, Pang JS, Ralph D (1996) Mathematical problems with equilibrium constraints. Cambridge University Press, Cambridge
[24] Luc DT (1989) Theory of vector optimization. Lecture notes in Ecological and Mathematics systems, vol 319. Springer, Berlin
[25] Luu DV (2014) Necessary and sufficient conditions for efficiency via convexificators. J Optim Theory Appl 160:510–526
[26] Luu DV (2016) Optimality conditions for local efficient solutions of vector equilibrium problems via convexificators and applications. J Optim Theory Appl 171:643–665
[27] Luu DV, Mai TV (2018) Optimality and duality in constrained interval-valued optimization. 4OR- Q. J Oper Res 16:311–327
[28] Luu DV, Hang DD (2015) On efficiency conditions for nonsmooth vector equilibrium problems with equilibrium constraints. Numer Funct Anal Optim 36:1622–1642
[29] Mangasarian OL (1969) Nonlinear programming. McGraw-Hill, New York
[30] Mond M, Weir T (1981) Generallized concavity and duality, Generallized concavity in optimization and economics. Academic Press, New York
[31] Movahedian N, Nabakhtian S (2010) Necessary and sufficient conditions for nonsmooth mathematical programs with equilibrium constraints. Nonlinear Anal 72:2694–2705
[32] Pandey Y, Mishra SK (2016) Duality for nonsmooth optimization problems with equilibrium constraints, using convexificators. J Optim Theory Appl 17:694–707
[33] Pandey Y, Mishra SK (2018) Optimality conditions and duality for semi-infinite mathematical programming problems with equilibrium constraints, using convexificators. Ann Oper Res 269:549–564
[34] Su TV, Hang DD (2019) Optimality conditions for the efficient solutions of vector equilibrium problems with constraints in terms of directional derivatives and applications. Bull Iran Math Soc 45(6):1619–1650
[35] Su TV, Dinh DH (2020) Duality results for interval-valued pseudoconvex optimization problem with equilibrium constraints with applications. Comput Appl Math 39(2):127–2020
[36] Su TV, Hien ND (2021) Studniarski’s derivatives and efficiency conditions for constrained vector equilibrium problems with applications. Optim 70(1):121–148. https://doi.org/10.1080/02331934.2019.1702985
[37] Su TV (2019) Second-order efficiency conditions for $$C^{1,1}-$$vector equilibrium problems in terms of contingent derivatives and applications. J Nonlinear Var Anal 3(3):317–332
[38] Su TV (2020) New second-order optimality conditions for vector equilibrium problems with constraints in terms of contingent derivatives. Bull Br Math Soc New Ser 51(2):371–395
[39] Suneja SK, Kohli B (2011) Optimality and duality results for bilevel programming problem using convexificators. J Optim Theory Appl 150:1–19
[40] Ye JJ, Zhu DL (1995) Optimality conditions for bilevel programming problems. Optim 33:9–27
[41] Ye JJ (2005) Necessary and sufficient optimality conditions for mathematical program with equilibrium constraints. J Math Anal Appl 307:350–369
[42] Wolfe P (1961) A duality theorem for nonlinear programming. Q J Appl Math 19:239–244