Research On Monotone ADMM-SQP Algorithms For Two-blocks Nonconvex Optimizations With General Linear And Nonlinear Equality Constraints

The alternating direction method with multipliers(ADMM)and sequen-tial quadratic programming(SQP)algorithm are very effective methods for solving constrained optimization problems.Although these two kinds of al-gorithms that more developed have been proposed in the twentieth century,they are still the research hotspots in the field of optimization.Because of the limitations of these two kinds of algorithms,there are still many academic problems worth studying.Based on the advantages of ADMM and SQP algorithms,this thesis proposes a new ADMM-SQP algorithm for the two-blocks nonconvex prob-lems with general linear constraints and nonlinear equality constraints.The algorithm's main li'ne is SQP,and the quadratic programming(QP)subprob-lem is decomposed into several smaller and completely independent ones by using the splitting idea of ADMM.The search direction is constructed by the optimal solution of the QP subproblem.The relaxed augmented Lagrange function is used as the merit function,and the Arimijo line search technique is used to generate new iteration points.Firstly,this paper studies the GLC-ADMM-SQP algorithm I and II for two-blocks problems with box and gen-eral linear constraints,and proves the convergence of the algorithm.When constructing the algorithm,the inequality constraints are transformed into e-quality constraints by introducing relaxation variable.The QP subproblem generated by relaxation variable has a simple structure and explicit optimal solution,so it does not need much computation.Secondly,box constraints are extended to the case of non-empty closed convex sets.A more widely applied GLC-ADMM-SQP algorithms ?+ and ?+ is proposed.Thirdly,inspired by the previous research ideas,this thesis constructs the NLC-ADMM-SQP al-gorithm for two-blocks problem with box and non-linear equality constraints,and prove its global convergence.Finally,the effectiveness of the algorithm is preliminarily verified by using the economic dispatching model of power system.