For the treatment of problems in one-parametric optimization we can use homotopie methodsbased on solving of a system of equations constructed from Lagrangian and active inequality constraints. But the active constraints are unknown in general. Another problem is theinaccuracy by the practical realization of the algorithm. The algorithm suggested in thisarticle works with an estimation of the active index set. This estimation will be changedif a test criterion is satisfied. Furthermore in certain situations a restart of the algorithm is possible. It will be shown, that the algorithm is successful under suitable assumptions.