Bertsimass and Sim propose a correlated model of data uncertainty in their well-known article (The price of robustness, 2002), but they assume that there are a few sources of uncertainty that affect data. Is there any way to use the covariance matrix of uncertain data without seeking for sources of uncertainty?
To the extend I understand the question, you can look at the paper by Mulvey-Vanderbei-Zenios on Robust optimization for large scale systems, Operations Research, Vol. 43 https://www.researchgate.net/publication/240310526_Robust_Optimization_of_Large-scale_Systems
Also, reducing the dimensionality of correlation matrices using principal component analysis as done in portfolio optimization (but with serious limiting assumptions) see Bertocci-Jacomett-Zenios in EJOR https://www.researchgate.net/publication/4872076_Risk_factor_analysis_and_portfolio_immunization_in_the_corporate_bond_market?ev=prf_pub
Hope these help.
Article Robust Optimization of Large-Scale Systems
Article Risk factor analysis and portfolio immunization in the corpo...
Thank you dear Dr Stavros Zenios
I have studied the famous article by Mulvey-Vanderbei-Zenios. Unfortunately the assumptions of my problem are different from the mentioned article. The robust optimization model in this paper is scenario based whereas I want to construct a robust model with respect to continuous uncertain parameters. Furthermore, I suppose that the uncertain parameters are allowed to change in a polyhedral perturbation set as Bertsimass and Sim supposed.
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