Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (4): 1079-1087.
Previous Articles Next Articles
Optimality Conditions for DC Composite Optimization Problems with Conical Constraints
Lingli Hu(
),Liping Tian(),Donghui Fang*()
- College of Mathematics and Statistics, Jishou University, Hunan Jishou 416000
-
Received:2020-09-29Online:2021-08-26Published:2021-08-09 -
Contact:Donghui Fang E-mail:847285225@qq.com;tianliping6889@163.com;fang@jsu.edu.cn -
Supported by:the NSFC(11861033);the NSF of Hunan Province(2020JJ4494);the Scientific Research Fund of Jishou University(Jd20008);the Scientific Research Fund of Jishou University(Jd20009)
CLC Number:
- O221.2
Cite this article
Lingli Hu,Liping Tian,Donghui Fang. Optimality Conditions for DC Composite Optimization Problems with Conical Constraints[J].Acta mathematica scientia,Series A, 2021, 41(4): 1079-1087.
share this article
Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks
| 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 |
| [1] | Chen Hongye, Fang Donghui, Wu Kexing. Optimality Conditions and Total Lagrange Dualities for Evenly Convex Optimization Problems [J]. Acta mathematica scientia,Series A, 2025, 45(4): 1255-1267. |
| [2] | Fang Donghui,Wang Junying. Characterizations of Approximate Solution and Approximate Duality for Quasiconvex Programming [J]. Acta mathematica scientia,Series A, 2025, 45(2): 640-652. |
| [3] | Hu Shanshan, He Suxiang. Optimality Conditions for Non-Negative Group Sparse Constrained Optimization Problems [J]. Acta mathematica scientia,Series A, 2024, 44(2): 500-512. |
| [4] | Jiaolang Wang,Donghui Fang. Approximate Optimality Conditions and Mixed Type Duality for a Class of Non-Convex Optimization Problems [J]. Acta mathematica scientia,Series A, 2022, 42(3): 651-660. |
| [5] | Tingwei Pan,Suxiang He. The Greedy Simplex Algorithm for Double Sparsity Constrained Optimization Problems [J]. Acta mathematica scientia,Series A, 2022, 42(3): 920-933. |
| [6] | Shengxin Hua,Guolin Yu,Wenyan Han,Xiangyu Kong. Characterization of Optimality to Constrained Vector Equilibrium Problems via Approximate Subdifferential [J]. Acta mathematica scientia,Series A, 2022, 42(2): 365-378. |
| [7] | Meng Li,Guolin Yu. Optimality of Robust Approximation Solutions for Uncertain Convex Optimization Problems [J]. Acta mathematica scientia,Series A, 2020, 40(4): 1007-1017. |
| [8] | Lingli Hu, Donghui Fang. Optimality Conditions for Composite Optimization Problems with Conical Constraints [J]. Acta mathematica scientia,Series A, 2018, 38(6): 1112-1121. |
| [9] | Huang Zhenggang. A New Notion of Generalized Subgradients and Its Properties [J]. Acta mathematica scientia,Series A, 2015, 35(5): 927-935. |
| [10] | LONG Xian-Jun. Optimality Conditions for Approximate Solutions on Nonconvex Vector Equilibrium Problems in Asplund Spaces [J]. Acta mathematica scientia,Series A, 2014, 34(3): 593-602. |
| [11] | YU Li, XU Xi-Hong. Generalized Gradient of Set-valued Optimization Problems and Optimality Conditions of Strong-efficient Solutions [J]. Acta mathematica scientia,Series A, 2012, 32(4): 685-690. |
| [12] | WANG Qi-Lin, LI Shng-Jie. Generalized |Higher-order Cone-directed Derivatives and Applications to Set-valued Optimization [J]. Acta mathematica scientia,Series A, 2011, 31(4): 902-909. |
| [13] |
Zhao Wenhui;Gao Yan.
Second-order Optimality Conditions for C1,1 Semidefinite Programming [J]. Acta mathematica scientia,Series A, 2008, 28(1): 155-163. |
| [14] | Hou Zhenmei; Liu Sanyang; Zhou Yong. The Optimality Conditions of Set-valued Vector Optimization on Super Efficiency [J]. Acta mathematica scientia,Series A, 2007, 27(1): 131-137. |
|