A Parametric Inertial Douglas-Rachford Splitting Algorithm And Its Applications

Douglas-Rachford splitting algorithm is a classical method for finding zeros of the sum of two maximally monotone operators.In recent years,many scholars have studied different forms of DR splitting algorithm and their applications in specific optimization problems,e.g.,parametric DR splitting algorithm,inertial DR splitting algorithm,etc..Enlightened by the existing work,we propose in this thesis a parametric inertial DouglasRachford splitting algorithm,the main innovation of which lies on the combination of parameter and inertial term.Employing fixed point theory of non-expansive mappings,we conduct convergence analysis for the iterative sequences generated by the algorithm,and study its applications in solving monotone inclusion problems involving mixtures of linearly composed and parallel-sum type operators.Numerical experiments show that,in comparison with the classical DR Splitting algorithm,the parametric inertial DR Splitting algorithm converges faster and is more flexible with parameter selection.