“…The perspectives of direct applications are numerous. In inverse problems, the symmetrized Bregman Gaps have been used, even if not always under this denomination, for nonlinear Cauchy problems in mechanics and the subsequent identification problems (nonlinear elasticity with small transformations, [9], plastic zones identification [10], cracks identification in contact mechanics [11]). As mentioned in the introduction, replacement of usual least-squares functionals in various algorithms or procedures in nonlinear mechanics and data-driven approaches can also be of interest and is seemingly straightforward.…”