Research On Inertial Proximal Peaceman-Rachford Splitting SQP Algorithm For Two-Block Nonconvex Optimization

With the advent of the big data era,large-scale optimization has become a pressing scientific problem across various fields.The idea of splitting methods,which is characterized by decomposition and dimensionality reduction,has attracted significant attention from both the mathematics and engineering fields,and its research and application are highly active.Therefore,it is very necessary to design efficient splitting methods with promising applications.The alternating direction method of multiplier(ADMM)and PeacemanRachford(PR)splitting method are both classical splitting algorithms.Meanwhile,the sequential quadratic programming(SQP)algorithm is one of the effective methods for solving smooth constrained optimization.It is favored for its fast convergence and computational effectiveness,especially for small to medium-scale problems.In this paper,based on the framework of the ADMM-SQP algorithm,we propose an inertial proximal PR splitting SQP algorithm for solving the two-block nonconvex optimization.The method incorporates the advantages of SQP algorithm and PR splitting method,and embeds inertial extrapolation step and proximal term in the design.Compared with the existing ADMMSQP algorithm,the Lagrangian multiplier of the method is updated twice by dual ascent type.Under suitable conditions,we prove the global convergence of the proposed algorithm,as well as its strong convergence and convergence rate under the assumption that the underlying functions satisfy the Kurdyka-?ojasiewicz property.Finally,preliminary numerical results illustrate the effectiveness and stability of the proposed method.