An inexact filter SQP algorithm for nonlinear programming

We present a sequential quadratic programming algorithm for solving equality and inequality constrained nonlinear programming problems. In each step of this algorithm, the steering direction is computed by minimizing a linear model of the constraint violation. Using the steering direction, a feasible quadratic programming subproblem is defined. After that, an inexact solution of the subproblem, namely the predictor direction, is computed. The predictor solution must satisfy some loose conditions which are necessary to prove the global convergence of the algorithm. The search direction in each step of our algorithm is an appropriate convex combination of the steering direction and the predictor direction. The search direction is a descent direction for the constraint violation and objective function. So using a backtracking procedure a step length can be found such that the new trial point is acceptable by the filter or the exact penalty function is reduced. Hence the global convergence of the algorithm can be proved. We implement this algorithm in the MATLAB environment. The preliminary numerical experiment on some test problem proves the efficiency of the presented algorithm.