On robust solutions to linear least squares problems affected by data uncertainty and implementation errors with application to stochastic signal modeling (Q1888347)

The robust solution to least squares problems with data uncertainties and coefficient quantization is considered. The investigation is resulted in approximate robust problems inspired by the important contributions of \textit{A. Ben-Tal} and \textit{A. Nemirovski} [Math. Oper. Res. 23, No.~4, 769--805 (1998; Zbl 0977.90052); SIAM J. Optim. 12, No.~3, 811--833 (2002; Zbl 1008.90034)]. The approximate robust counterpart problems are semidefinite programming problems efficiently solved by polynomial interior point algorithms. To illustrate the performance of the proposed framework, the well known digital signal processing application of ARMA modeling is used. Some experimental results are given to demonstrate that the robust least squares solution approach provides significantly more stable solutions even in the presence of coefficient quantization effects. Thus, the robust least squares approach addresses the right issues in the implementation of ARMA signal modeling, and provides reliable models.