This explains the necessity of highly sophisticated mathematical algorithms that will account for the inverse problem and its ill-posedness.

"Instability and ill-posedness in some friction problems" (with F.M.F. Simões), Int.

Regularized optimization problems are especially relevant in the high dimensional regime since regularization is a natural mechanism to overcome ill-posedness and to encourage parsimony in the optimal solution, e.g., sparsity and low rank.