一类两阶段自适应鲁棒多目标规划的对偶性刻画

Abstract

Abstract:

In this paper, we deal with a class of two-stage adjustable robust multi-objective programming problems with spectrahedral uncertainty data in both objective and constraints. We first establish a Farkas lemma for a two-stage adjustable robust multiobjective programming with affine adjustable variable. Then, we propose a semidefinite programming dual problem for this multiobjective programming problem. Furthermore, in terms of the obtained Farkas lemma, we explore duality properties between them.

Key words: Adjustable robust programming, Farkas lemma, Duality

CLC Number:

O221.6

Huang Jiayi, Sun Xiangkai. Duality Characterizations for a Class of Two-Stage Adjustable Robust Multiobjective Programming[J].Acta mathematica scientia,Series A, 2024, 44(1): 185-194.

Trendmd

References 20

[1]	Ben-Tal A, Nemirovski A. Robust optimization-methodology and applications. Math Program, 2002, 92: 453-480 doi: 10.1007/s101070100286
[2]	Ben-Tal A, EI Ghaoui L, Nemirovski A. Robust Optimization. Princeton: Princeton university press, 2009.
[3]	Goberna M A, Jeyakumar V, Li G, López M A. Robust linear semi-infinite programming duality under uncertainty. Math Program, 2013, 139: 185-203 doi: 10.1007/s10107-013-0668-6
[4]	Sun X, Tang L, Zeng J. Characterizations of approximate duality and saddle point theorems for nonsmooth robust vector optimization. Numer Funct Anal Optim, 2020, 41: 462-482 doi: 10.1080/01630563.2019.1660891
[5]	叶冬平, 方东辉. 鲁棒复合优化问题的 Lagrange 对偶. 数学物理学报, 2020, 40A(4): 1095-1107
	Ye D P, Fang D H. Lagrange duality of robust composite optimization problems. Acta Math Sci, 2020, 40A(4): 1095-1107
[6]	Ben-Tal A, Goryashko A, Guslitzer E, Nemirovski A. Adjustable robust solutions of uncertain linear programs. Math Program, 2004, 99: 351-376 doi: 10.1007/s10107-003-0454-y
[7]	Delage E, Iancu D A. Robust multistage decision making. Informs Tutor Oper Res, 2015, 2: 20-46
[8]	Ruiter F, Ben-Tal A, Brekelmans R, Hertog D. Robust optimization of uncertain multistage inventory systems with inexact data in decision rules. Comput Manag Sci, 2017, 14: 45-66 doi: 10.1007/s10287-016-0253-6
[9]	Zhen J, Hertog D D, Sim M. Adjustable robust optimization via Fourier-Motzkin elimination. Oper Res, 2018, 66: 1086-1100 doi: 10.1287/opre.2017.1714
[10]	Jeyakumar V, Li G, Woolnough D. Quadratically adjustable robust linear optimization with inexact data via generalized S-lemma: Exact second-order cone program reformulations. EURO J Comput Optim, 2021, 9: 100019 doi: 10.1016/j.ejco.2021.100019
[11]	Chuong T D, Jeyakumar V, Li G, Woolnough D. Exact SDP reformulations of adjustable robust linear programs with box uncertainties under separable quadratic decision rules via SOS representations of non-negativity. J Global Optim, 2021, 81: 1095-1117 doi: 10.1007/s10898-021-01050-x
[12]	Woolnough D, Jeyakumar V, Li G. Exact conic programming reformulations of two-stage adjustable robust linear programs with new quadratic decision rules. Optim Lett, 2021, 15: 25-44 doi: 10.1007/s11590-020-01595-y
[13]	Chuong T D, Jeyakumar V. Adjustable robust multiobjective linear optimization: Pareto optimal solutions via conic programming. Ann Oper Res, 2022. https://doi.org/10.1007/s10479-022-05104-5
[14]	Chuong T D, Jeyakumar V, Li G, Woolnough D. Exact dual semi-definite programs for affinely adjustable robust SOS-convex polynomial optimization problems. Optimization, 2022, 71: 3539-3569 doi: 10.1080/02331934.2021.1902521
[15]	de Ruiter F J C T, Zhen J, den Hertog D. Dual approach for two-stage robust nonlinear optimization. Oper Res, 2023, 71: 1794-1799 doi: 10.1287/opre.2022.2289
[16]	Ramana M, Goldman A J. Some geometric results in semidefinite programming. J Global Optim, 1995, 7: 33-50 doi: 10.1007/BF01100204
[17]	Vinzant C. What is a spectrahedron? Notices Amer Math Soc, 2014, 61: 492-494
[18]	Kuroiwa D, Lee G M. On robust multiobjective optimization. Vietnam J Math, 2012, 40: 305-317
[19]	Chuong T D. Robust alternative theorem for linear inequalities with applications to robust multiobjective optimization. Oper Res Lett, 2017, 45: 575-580 doi: 10.1016/j.orl.2017.09.002
[20]	Chuong T D. Linear matrix inequality conditions and duality for a class of robust multiobjective convex polynomial programs. SIAM J Optim, 2018, 28: 2466-2488 doi: 10.1137/17M1143484

Duality Characterizations for a Class of Two-Stage Adjustable Robust Multiobjective Programming

RichHTML

PDF (PC)

Abstract

Cite this article

share this article

References 20

Related Articles 15

Metrics

Comments

Recommended 10

[1]	Xie Feifei, Fang Donghui. Approximate Farkas Lemma and Approximate Duality for Fractional Optimization Problems [J]. Acta mathematica scientia,Series A, 2023, 43(1): 305-320.
[2]	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.
[3]	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.
[4]	Xinyi Feng,Xiangkai Sun. Characterizations of Farkas Lemmas for a Class of Fractional Optimization with DC Functions [J]. Acta mathematica scientia,Series A, 2021, 41(3): 827-836.
[5]	Juan Wang,Jie Zhao. Homogenization of the Oscillating Robin Mixed Boundary Value Problems [J]. Acta mathematica scientia,Series A, 2021, 41(1): 81-90.
[6]	Dongping Ye,Donghui Fang. Lagrange Dualities for Robust Composite Optimization Problems [J]. Acta mathematica scientia,Series A, 2020, 40(4): 1095-1107.
[7]	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.
[8]	Amir KHOSRAVI, Morteza MIRZAEE AZANDARYANI. APPROXIMATE DUALITY OF g-FRAMES IN HILBERT SPACES [J]. Acta mathematica scientia,Series A, 2014, 34(3): 639-652.
[9]	CUI Huan-Huan. An Iterative Sequence with Norm Convergence for Accretive Operators in Banach Spaces [J]. Acta mathematica scientia,Series A, 2014, 34(3): 755-759.
[10]	GUO Shuang-Jian, WANG Shuan-Hong. Crossed Products of Weak Hopf Group Coalgebras [J]. Acta mathematica scientia,Series A, 2014, 34(2): 327-337.
[11]	CHEN Jia-Wei, LI Jun, WANG Jing-Nan. Optimality Conditions and Duality for Nonsmooth Multiobjective Optimization Problems with Cone Constraints [J]. Acta mathematica scientia,Series A, 2012, 32(1): 1-12.
[12]	YU Guo-Lin, LIU Wan-Li. Henig Proper Efficiency in the ic-Conen-Convexlike Set-valued Optimization Problems [J]. Acta mathematica scientia,Series A, 2009, 29(3): 800-809.
[13]	Xiao Xuemei; Zhu Yucan. Duality Principles of Frames in Banach Spaces [J]. Acta mathematica scientia,Series A, 2009, 29(1): 94-102.
[14]	Chen Zhe. Generalized Augmented Lagrangian Duality Theory and Applications in Vector Optimization Problems [J]. Acta mathematica scientia,Series A, 2008, 28(3): 570-577.
[15]	Xu Huiming;Liu Taishun. Boundary Values and Duality of Some Spaces of Holomorphic [J]. Acta mathematica scientia,Series A, 2006, 26(1): 113-123.