Local Convergence Analysis of Stabilized Sequential Quadratic Programming Methods for Optimization Problems in Banach Spaces

Abstract. This paper presents a stabilized sequential quadratic programming (SQP) method for solving optimization problems in Banach spaces. The optimization problem considered in this study has a general form that enables us to represent various types of optimization problems and is particularly applicable to optimal control problems, obstacle problems, and shape optimization problems. Several SQP methods have been proposed for optimization problems in Banach spaces with specific structures. However, local convergence analysis of SQP-type methods for general problems, such as those considered in this study, is limited. We focus on the local behavior of the proposed stabilized SQP method and prove its local quadratic convergence under reasonable assumptions. Finally, numerical experiments are provided.