Scopus

Duality results for interval-valued pseudoconvex optimization problem with equilibrium constraints with applications

Năm XB 2020 Tạp chí / Hội thảo Computational and Applied Mathematics Volume 39 (2) DOI / Link https://doi.org/10.1007/s40314-020-01153-3 ↗

Tác giả

Tài liệu tham khảo

[1] Aubin J-P (1981) Contingent derivatives of set-valued maps and existence of solutions to nonlinear inclusions and differential inclusions. In: L. Nachbin (ed) Advances in mathematics supplementary studies 7A. Academic Press, New York, pp 159–229

[2] Aubin J-P, Frankowska H (1990) Set-valued analysis. Birkhauser, Boston

[3] Bhurjee AK, Panda G (2015) Multi-objective interval fractional programming problems: an approach for obtaining efficient solutions. Opsearch 52:156–167

[4] Bhurjee AK, Panda G (2016) Sufficient optimality conditions and duality theory for interval optimization problem. Ann Oper Res 243:335–348

[5] Bot RI, Grad S-M (2010) Wolfe duality and Mond-Weir duality via perturbations. Nonlinear Anal Theory Methods Appl 73(2):374–384

[6] Bot RI, Grad S-M, Wanka G (2009) Duality in vector optimization. Springer, Berlin

[7] Bonnel H, Iusem AN, Svaiter BF (2005) Proximal methods in vector optimization. SIAM J Optim 15(4):953–970

[8] Gong XH (2010) Scalarization and optimality conditions for vector equilibrium problems. Nonlinear Anal 73:3598–3612

[9] Iusem AN, Mohebbi V (2019) Extragradient methods for vector equilibrium problems in Banach spaces. Numer Funct Anal Optim 40(9):993–1022

[10] Jahn J, Khan AA (2003) Some calculus rules for contingent epiderivatives. Optimization 52(2):113–125

[11] Jahn J, Khan AA (2013) The existence of contingent epiderivatives for set-valued maps. Appl Math Lett 16:1179–1185

[12] Jahn J, Rauh R (1997) Contingent epiderivatives and set-valued optimization. Math Methods Oper Res 46:193–211

[13] Jayswal A, Stancu-Minasian I, Ahmad I (2011) On sufficiency and duality for a class of interval-valued programming problems. Appl Math Comput 218:4119–4127

[14] Jayswal A, Stancu-Minasian I, Banerjee J (2016) Optimality conditions and duality for interval-valued optimization problems using convexificators. Rend Cire Mat Palermo 65:17–32

[15] Jiménez B, Novo V (2008) First order optimality conditions in vector optimization involving stable functions. Optimization 57(3):449–471

[16] Jiménez B, Novo V, Sama M (2009) Scalarization and optimality conditions for strict minimizers in multiobjective optimization via contingent epiderivatives. J Math Anal Appl 352:788–798

[17] López MA, Still G (2007) Semi-infinite programming. Eur J Oper Res 180:491–518

[18] Luc DT (1989) Theory of vector optimization. In: Lecture notes in economics and mathematics systems, vol 319. Springer, Berlin

[19] Luc DT (1991) Contingent derivatives of set-valued maps and applications to vector optimization. Math Program 50:99–111

[20] Luo ZQ, Pang JS, Ralph D (1996) Mathematical problems with equilibrium constraints. Cambridge University Press, Cambridge

[21] Luu DV, Mai TT (2018) Optimality and duality in constrained interval-valued optimization, 4OR- Q. J Oper Res 16:311–327

[22] Luu DV, Hang DD (2015) On efficiency conditions for nonsmooth vector equilibrium problems with equilibrium constraints. Numer Funct Anal Optim 36:1622–1642

[23] Luu DV, Su TV (2018) Contingent derivatives and necessary efficiency conditions for vector equilibrium problems with constraints. RAIRO Oper Res 52:543–559

[24] Mangasarian OL (1969) Nonlinear Programming. McGraw-Hill, New York

[25] Mangasarian OL (1965) Pseudo-convex functions. J SIAM Control Ser A 3:281–290

[26] Mond M, Weir T (1981) Generallized concavity and duality. In: Generallized concavity in optimization and economics. Academic Press, New York

[27] Movahedian N, Nabakhtian S (2010) Necessary and sufficient conditions for nonsmooth mathematical programs with equilibrium constraints. Nonlinear Anal 72:2694–2705

[28] More RE (1983) Methods and applications for interval analysis. SIAM, Philadelphia

[29] Pandey Y, Mishra SK (2016) Duality for nonsmooth optimization problems with equilibrium constraints, using convexificators. J Optim Theory Appl 17:694–707

[30] 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

[31] Rodríguez-Marín L, Sama M (2007) About contingent epiderivatives. J Math Anal Appl 327:745–762

[32] Rodríguez-Marín L, Sama M (2007) Variational characterization of the contingent epiderivative. J Math Anal Appl 335:1374–1382

[33] Su TV (2016) Optimality conditions for vector equilibrium problems in terms of contingent epiderivatives. Numer Funct Anal Optim 37:640–665

[34] 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

[35] Su TV, Hien ND (2019) Necessary and sufficient optimality conditions for constrained vector equilibrium problems using contingent hypoderivatives. Optim Eng. https://doi.org/10.1007/s11081-019-09464-z (to appear 2019)

[36] Suneja SK, Kohli B (2011) Optimality and duality results for bilevel programming problem using convexificators. J Optim Theory Appl 150:1–19

[37] Ye J (2005) J: Necessary and sufficient optimality conditions for mathematical program with equilibrium constraints. J Math Anal Appl 307:350–369

[38] Wolfe P (1961) A duality theorem for nonlinear programming. Q J Appl Math 19:239–244

[39] Wu H-C (2008) On interval-valued nonlinear programming problems. J Math Anal Appl 338:299–316