| 1 |
Boţ R I , Grad S M , Wanka G . On strong and total Lagrange duality for convex optimization problems. J Math Anal Appl, 2008, 37, 1315- 1325
|
| 2 |
Boţ R I , Grad S M , Wanka G . New regularity conditions for strong and total Fenchel-Lagrange duality in infinite dimensional spaces. Nonlinear Anal, 2008, 69, 323- 336
doi: 10.1016/j.na.2007.05.021
|
| 3 |
Fang D H , Li C , Ng K F . Constraint qualifications for optimality conditions and total Lagrangian dualities in convex infinite programming. Nonlinear Anal, 2010, 73, 1143- 1159
doi: 10.1016/j.na.2010.04.020
|
| 4 |
Jeyakumar V , Lee G M . Complete characterization of stable Farkas' lemma and cone-convex programming duality. Math Program Ser A, 2008, 14, 335- 347
doi: 10.1007/s10107-007-0104-x
|
| 5 |
Sun X K , Chai Y . Optimality conditions for DC fractional programming problems. Advan Math, 2014, 18, 9- 28
|
| 6 |
Li G , Zhou Y Y . The stable Farkas lemma for composite convex functions in infinite dimensional spaces. Acta Math Appl Sin, 2015, 31, 677- 692
doi: 10.1007/s10255-015-0493-1
|
| 7 |
孙祥凯. 复合凸优化问题全对偶性的等价刻画. 吉林大学学报, 2015, 53, 33- 36
|
|
Sun X K . Some characterizations of total duality for a composed convex optimization. Journal of Jilin University, 2015, 53, 33- 36
|
| 8 |
方东辉, 王梦丹. 锥约束复合优化问题的Lagrange对偶. 系统科学与数学, 2017, 37, 203- 211
doi: 10.12341/jssms13054
|
|
Fang D H , Wang M D . Study on the Lagrange dualities for composite optimization problems with conical constraints. J Sys Sci Math Scis, 2017, 37, 203- 211
doi: 10.12341/jssms13054
|
| 9 |
Long X J , Sun X K , Peng Z Y . Approximate optimality conditions for composite convex optimization problems. J Oper Res Soc, 2017, 5, 469- 485
doi: 10.1007/s40305-016-0140-4
|
| 10 |
胡玲莉, 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
doi: 10.3969/j.issn.1003-3998.2018.06.008
|
|
Hu L L , Fang D H . Optimality conditions for composite optimization problems with conical constraints. Acta Math Sci, 2018, 38A (6): 1112- 1121
doi: 10.3969/j.issn.1003-3998.2018.06.008
|
| 11 |
Dinh N , Vallet G , Nghia T T A . Farkas-type results and duality for DC programs with convex constraints. J Convex Anal, 2008, 15, 235- 262
|
| 12 |
Sun X K , Li S J , Zhao D . Duality and Farkas-type results for DC infinite programming with inequality constraints. Taiwanese Journal of Mathematics, 2013, 17, 1227- 1244
|
| 13 |
Sun X K , Long X J , Li M H . Some characterizations of duality for DC optimization with composite functions. Optim, 2017, 66, 1425- 1443
doi: 10.1080/02331934.2017.1338289
|
| 14 |
Tian L P , Wang M D , Fang D H . Zero duality gap properties for DC composite optimazation problem. J Nonlinear Convex Anal, 2019, 20, 513- 525
doi: 10.1186/s13660-019-2141-4
|
| 15 |
Fang D H , Zhang Y . Optimality conditions and total dualities for conic programming involving composite function. Optim, 2020, 69, 305- 327
doi: 10.1080/02331934.2018.1561695
|
| 16 |
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, 351- 376
doi: 10.1007/s10957-018-1219-3
|
| 17 |
Fang D H , Gong X . Extended Farkas lemma and strong duality for composite optimization problems with DC functions. Optim, 2017, 66, 179- 196
doi: 10.1080/02331934.2016.1266628
|
| 18 |
Zǎlinescu C . Convex Analysis in General Vector Spaces. New Jersey: World Scientific, 2002
|
| 19 |
Mordukhovich B S , Nam N M , Yen N D . Frchet subdifferential calculus and optimality conditions in nondifferentiable programming. Optim, 2006, 55, 685- 708
doi: 10.1080/02331930600816395
|
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