Robust Optimization Model for a Class of Uncertain Linear Programs Weimin Miao 1 , Hongxia Yin 1⋆ , Donglei Du 2⋆⋆ , and Jiye Han 3⋆⋆⋆ 1 School of Mathematical Sciences, Graduate University of Chinese Academy of Sciences, P.O. Box 4588, Beijing 100049, China wmmiao@hotmail.com, hxyin@gucas.ac.cn 2 Faculty of Business Administration, University of New Brunswick, P.O.Box 4400, Fredericton, NB, E3B 5A3, Canada ddu@unb.ca 3 Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China jiyehan@vip.sina.com Abstract. In the paper, we propose a tractable robust counterpart for solving the uncertain linear optimization problem with correlated uncer- tainties related to a causal ARMA(p, q) process. This explicit treatment of correlated uncertainties under a time series setting in robust optimiza- tion is in contrast to the independent or simple correlated uncertainties assumption in existing literature. under some reasonable assumptions, we establish probabilistic guarantees for the feasibility of the robust so- lution. Finally, we provide a numerical method for the selection of the parameters which controls the tradeoff among the tractability, the ro- bustness and the optimality of the robust model. 1 Introduction Robust optimization is an important technique for investigating optimization problems with uncertainties. We consider the uncertain linear optimization prob- lem max  c ′ x| ˜ Ax ≤ ˜ b  , (1) where x and c are real vectors in R n , ˜ A ∈R m×n and ˜ b ∈R m are uncertain ma- trix and vector with entries belonging to a known set U . The robust counterpart of problem (1) is given by max  c ′ x| ˜ Ax ≤ ˜ b, ∀( ˜ A, ˜ b) ∈U  . (2) ⋆ The author’s research is supported by the National Natural Science Foundation of China 10671203,70531040, and 70621001. ⋆⋆ The author’s research is supported in part by NSERC grant 283103, and URF, FDF at UNB. ⋆⋆⋆ The author’s research is supported by the National Natural Science Foundation of China NSF 10401038.