An infeasible SSLE filter algorithm for inequality constrained optimization

The inequality constrained optimization problem is reformulated as its equivalent equality constrained optimization problem. It is proved that they have the same Karush-Kuhn-Tucker(KKT) conditions under some suitable conditions. The multiplier of the equivalent equality constrained optimization problem needs to be nonnegative. Therefore, its KKT conditions are different from those of the general equality constrained optimization problem. An infeasible sequential system of linear equations(SSLE) filter algorithm is presented to solve this type of problem. It only needs to solve two systems of linear equations with the same nonsingular coefficient matrix, which results in a less computation. The global convergence of the algorithm is established under suitable conditions. Some numerical results are also reported.