鲁棒复合优化问题的Lagrange对偶

Acta mathematica scientia,Series A ›› 2020, Vol. 40 ›› Issue (4): 1095-1107.

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Lagrange Dualities for Robust Composite Optimization Problems

Dongping Ye(),Donghui Fang*()

^{College of Mathematics and Statistics, Jishou University, Hunan Jishou 416000}

Received:2019-07-23 Online:2020-08-26 Published:2020-08-20
Contact: Donghui Fang E-mail:1441638656@qq.com;dh_fang@jsu.edu.cn
Supported by:
the NSFC(11861033);the NSF of Hunan Province(2020JJ4494);the Scientific Research Fund of Hunan Provincial Education Department(17A172);the Scientific Research Fund of Jishou University(Jdy19001)

Abstract

Abstract:

By using the properties of the epigraph of the conjugate functions, two new constraint qualifications are given. Under these constraint qualifications, the zero duality, the strong duality, the stable zero duality and the stable strong duality between robust composite optimization problem and its Lagrange dual problems are established, which extend and improve the corresponding results in the previous papers.

Key words: Robust composite optimization problem, Constraint qualification, Zero duality, Strong duality

CLC Number:

O224

Dongping Ye,Donghui Fang. Lagrange Dualities for Robust Composite Optimization Problems[J].Acta mathematica scientia,Series A, 2020, 40(4): 1095-1107.

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References 20

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[1]	Donghui Fang,Liping Tian,Xianyun Wang. Strong Fenchel-Lagrange Duality for Convex Optimization Problems with Composite Function [J]. Acta mathematica scientia,Series A, 2020, 40(1): 20-30.
[2]	Donghui Fang,Weilin Liu. The Farkas Lemmas for Fractional Optimization Problem with Composite Functions [J]. Acta mathematica scientia,Series A, 2018, 38(5): 842-854.
[3]	Chen Zhe. Generalized Augmented Lagrangian Duality Theory and Applications in Vector Optimization Problems [J]. Acta mathematica scientia,Series A, 2008, 28(3): 570-577.

Lagrange Dualities for Robust Composite Optimization Problems

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