Feasibility refinement in sequential quadratic programming using parametric sensitivity analysis

In this paper we present results that extend the sequential quadratic programming (SQP) algorithm with an additional feasibility refinement based on parametric sensitivity derivatives. The refinement is applicable without restriction on the problem dimensions in sparse SQP solvers. Parametric sensitivity analysis is a tool for post optimality analysis of the solution of a nonlinear optimization problem. For the refinement approach we apply this technique on the quadratic subproblems in order to improve the overall algorithm. The sensitivity derivatives required for this approach can be computed without noticeable computational effort as the system of linear equations to be solved coincides with the system already solved for the search direction computation. For similar algorithms in the context of post optimality analysis a linear rate of convergence has been proven and therefore an extrapolation method is applied to speed up the process. The presented algorithm has been integrated into the nonlinear program (NLP) solver WORHP and we perform a numerical study to evaluate different termination criteria for the proposed algorithm. Furthermore, numerical results on the CUTEst test set are shown.