A new approach to solve non-regular constrained optimization problems. An application to optimal provision of public inputs.

This paper describes a new method for solving non-regular constrained optimization problems when standard methodologies do not work properly. Our method (the Rational Iterative Multisection Procedure, RIMP) consists of different stages that can be interpreted as different requirements of precision by obtaining the optimal solution. We have performed an application of RIMP to the case of public inputs provision under two tax settings. We prove that the RIMP and the standard Newton-Raphson (NR) method achieve the same results with regular optimization problems while the RIMP takes advantage over NR when facing non-regular optimization problems.