Global convergence of a tri-dimensional filter SQP algorithm based on the line search method

In this paper, we propose a new filter line search SQP method in which the violations of equality and inequality constraints are considered separately. Thus the filter in our algorithm is composed by three components: objective function value, equality and inequality constraints violations. The filter with three components accepts reasonable steps flexibly, comparing that with two components. The new filter shares some features with the Chin and Fletcher's approach, namely the “slanting envelope” and the “inclusion property”. Under mild conditions, the filter line search SQP method is proven to be globally convergent. Numerical experiments also show the efficiency of our method.