Applying Infeasible Interior Point Method to SQP for Constrained Nonlinear Programming

Active set (AS) method suffers deteriorating performance and premature convergence when it is faced with a nonlinear programming problem (NLP) consisting of several inequality constraints. Thus, we propose an SQP/IPM algorithm that uses infeasible interior point method (IIPM) for solving quadratic programming (QP) subproblems. In this approach inequality constraints can be solved directly, alleviating the burden for choosing a feasible starting point necessary for efficient convergence to optimal active set. At every iteration k, we evaluate step length adaptively via a simple line search or a quadratic search algorithm depending on the QP subproblem. Benchmark NLPs are used for performance assessment and our SQP/IPM algorithm proves to be efficient and promising.