A new inexact SQP algorithm for nonlinear systems of mixed equalities and inequalities (Q1656673)

It is known that the traditional inexact SQP method can only solve a nonlinear equality constrained optimization problem. In this paper, the authors present the new inexact SQP method with an affine scaling technique for a special nonlinear optimization problem with equality and bound constraints, and get so a solution of nonlinear systems of mixed equalities and inequalities. The proposed method has the following properties: it extends the theory of an inexact SQP method for nonlinear optimization with equality and bound constraints, the dwindling filter is employed in the new algorithm, thus providing a new idea for solving nonlinear systems of mixed equalities and inequalities and the filter algorithm does not need a feasibility restoration phase which requires a lot of computations in traditional filter methods. The global convergence is considered, too.The preliminary numerical results show the efficiency of the presented algorithm.