| 1 | Boncea H V , Grad S M . Characterizations of ε-duality gap statements for composed optimization problems. Nonlinear Anal, 2013, 92, 96- 107 | | 2 | Bo? R I , Csetnek E R , Wanka G . Regularity conditions via quasi-relative interior in convex programming. SIAM J Optim, 2008, 19, 217- 233 | | 3 | Bo? R I , Grad S M , Wanka G . A new constraint qualification for the formula of the subdifferential of composed convex functions in infinite dimensional spaces. Math Nachr, 2008, 281, 1088- 1107 | | 4 | Bo? R I , Grad S M , Wanka G . Generalized Moreau-Rockafellar results for composed convex functions. Optim, 2009, 58, 917- 933 | | 5 | Bo? R I, Grad S M, Wanka G. Duality in Vector Optimizaition. New York: Springer, 2009 | | 6 | Bo? R I , Wanka G . A weaker regularity condition for subdifferential calculus and Fenchel duality in infinite dimensional spaces. Nonlinear Anal, 2006, 64, 2787- 2804 | | 7 | Dinh N , Vallet G , Volle M . Functional inequalities and theorems of the alternative involving composite functions. J Glob Optim, 2014, 59, 837- 863 | | 8 | Fang D H , Anasri Q H , Zhao X P . Constraint qualifications and zero duality gap properties in conical programming involving composite functions. J Nonlinear Convex Anal, 2018, 19 (1): 53- 69 | | 9 | 方东辉, 刘伟玲. 带复合函数的分式优化问题的Farkas引理. 数学物理学报, 2018, 38A (5): 842- 854 | | 9 | Fang D H , Liu W L . The farkas lemmas for fractional optimization problem with composite functions. Acta Math Sci, 2018, 38A (5): 842- 854 | | 10 | 胡伶俐, 方东辉. 带锥约束的复合优化问题的最优性条件. 数学物理学报, 2018, 38A (6): 1112- 1121 | | 10 | Hu L L , Fang D H . Optimality conditions for composite optimization problems with conical constraints. Acta Math Sci, 2018, 38A (6): 1112- 1121 | | 11 | Fang D H , Li C , Ng K F . Constraint qualifications for extended Farkas's lemmas and Lagrangian dualities in convex infinite programming. SIAM J Optim, 2009, 20 (3): 1311- 1332 | | 12 | Fang D H , Gong X . Extended Farkas lemma and strong duality for composite optimization problems with DC functions. Optim, 2017, 66 (2): 179- 196 | | 13 | Fang D H , Zhang Y . Extended Farkas's lemmas and strong dualities for conic constraint problem involving composite functions. J Optim Theory Appl, 2018, 176 (2): 351- 376 | | 14 | Li C , Fang D H , López G , López M A . Stable and total Fenchel duality for convex optimization problems in locally convex spaces. SIAM J Optim, 2009, 20, 1032- 1051 | | 15 | Long X J , Sun X K , Peng Z Y . Approximate optimality conditions for composite convex optimization problems. J Oper Res Soc China, 2017, 5, 469- 485 | | 16 | Li G , Zhou Y Y . The stable Farkas lemma for composite convex functions in infinite dimensional spaces. Acta Math Appl Sinica, 2015, 31, 677- 692 | | 17 | Zǎlinescu C. Convex Analysis in General Vector Spaces. New Jersey: World Scientific, 2002 | | 18 | Zhou Y Y , Li G . The Toland-Fenchel-Lagrange duality of DC programs for composite convex functions. Numer Algebra Contr Optim, 2014, 4, 9- 23 |
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