A Sequential Quadratic Programming Algorithm with a Piecewise Linear Merit Function

A sequential quadratic programming algorithm for solving nonlinear programming problems is presented. The new feature of the algorithm is related to the definition of the merit function. Instead of using one penalty parameter per iteration and increasing it as the algorithm progresses, we suggest that a new point is to be accepted if it stays sufficiently below the piecewise linear function defined by some previous iterates on the $(f; ||C||^2_2)$ space. Therefore, the penalty parameter is allowed to decrease between successive iterations. Besides, one need not to decide how to update the penalty parameter. This approach resembles the filter method introduced by Fletcher and Leyffer [7], but it is less tolerant since a merit function is still used.