Interior-point methods are well suited for solving convex non-smooth optimization problems which arise for instance in problems involving plasticity or contact conditions. This work attempts at extending their field of application to optimization problems involving either smooth but non-convex or non-smooth but convex objectives or constraints. A typical application for such kind of problems is finite-strain elastoplasticity which we address using a total Lagrangian formulation based on logarithmic strain measures. The proposed interior-point algorithm is implemented and tested on 3D examples involving plastic collapse and geometrical changes. Comparison with classical Newton-Raphson/return mapping methods shows that the interior-point method exhibits good computational performance , especially in terms of convergence robustness. Similarly to what is observed for convex small-strain plasticity, the interior-point method is able to converge for much larger load steps than classical methods.