Robust Solutions to Least-Squares Problems with Uncertain Data

Robust Solutions to Least-squares Problems with Uncertain Data

We consider least-squares problems where the coefficient matrices A, b are unknown but bounded. We minimize the worst-case residual error using (convex) second-order cone programming, yielding an algorithm with complexity similar to one singular value decomposition of A. The method can be interpreted as a Tikhonov regularization procedure, with the advantage that it provides an exact bound on t...

Robust solutions to uncertain weighted least squares problems ∗

Robust optimization is a rapidly developing methodology for handling optimization problems affected by non-stochastic uncertain-but-bounded data perturbations. In this paper, we consider the weighted least squares problems where the coefficient matrices and vector belong to different uncertain bounded sets. We introduce the robust counterparts of these problems and reformulate them as the tract...

Robust solutions of Linear Programming problems contaminated with uncertain data

Optimal solutions of Linear Programming problems may become severely infeasible if the nominal data is slightly perturbed. We demonstrate this phenomenon by studying 90 LPs from the well-known NETLIB collection. We then apply the Robust Optimization methodology (Ben-Tal and Nemirovski [1-3]; El Ghaoui et al. [5,6]) to produce “robust” solutions of the above LPs which are in a sense immuned agai...

Near optimal solutions to least-squares problems with stochastic uncertainty

In this paper, we consider least-squares (LS) problems where the regression data is affected by parametric stochastic uncertainty. In this setting, we study the problem of minimizing the expected value with respect to the uncertainty of the LS residual. For general nonlinear dependence of the data on the uncertain parameters, determining an exact solution to this problem is known to be computat...

The least squares fit of a hyperplane to uncertain data