ADMM-SQP Algorithms For Nonconvex Block Optimization With Linear Constraints

This dissertation studies linear constrained nonconvex block optimiza-tion,which have a very wide range of applications in such important fields as data mining,signal processing,wireless network and smart grid supply,etc.Because the objective function of the problem studied in this dissertation has separable structure.Therefore,it is of important scientific significance and application value to explore its special and effective solution ideas and methods.The alternating direction method of multipliers(ADMM)is one of the effective ways for solving large-scale two-block linearly constrained convex minimization model.It has the decomposition of dimensionality and simple structure of the powerful features.The idea of sequential quadratic program-ming(SQP)is an important way to study and construct a smooth non-convex optimization algorithm with good numerical and fast convergence speed,E-specially for small and medium-sized issues.This dissertation is based on the ADMM and SQP methods,Focus on the study of linear constrained par-titioned blocks non-convex optimization of a new efficient algorithm.First of all,it is aimed at the problem of separation and Optimization for two par-tition blocks,The main idea of sequence quadratic programming,Introduce ADMM in solving its quadratic programming(QP)sub-problems,The QP is decomposed into two independent and small-scale QP to solutions,a new it-eration point is generated by Armijo line search with augmented Lagrangian function as a benefit function.Therefore,a new type of ADMM-SQP al-gorithm is constructed.Under appropriate assumptions,the fitness of the algorithm is proved,and under weaker conditions,we analyze the global convergence of the algorithm in the usual sense.Secondly,The two-block optimization is extended to study the multi block optimization problem,and global convergence of ADMM-SQP algorithm is established.Last,the nu-merical tests validate our method with the help of MATLAB for a set of test problems.