线性约束两分块非凸优化的ADMM-SQP算法

摘要

Based on the alternating direction method of multipliers (ADMM) and the sequential quadratic programming (SQP) method,this paper proposes a new efficient algorithm for two blocks nonconvex optimization with linear constrained.Firstly,taking SQP thought as the main line,the quadratic programming (QP) is decomposed into two independent small scale QP according to ADMM idea.Secondly,the new iteration point of the prime variable is generated by Armijo line search for the augmented Lagrange function.Finally,the dual variables are updated by an explicit expression.Thus,a new ADMM-SQP algorithm is constructed.Under the weaker conditions,the global convergence of the algorithm is analyzed.Some preliminary numerical results are reported to support the efficiency of the new algorithm.%基于乘子交替方向法(ADMM)和序列二次规划(SQP)方法思想,致力于研究线性约束两分块非凸优化的新型高效算法.首先,以SQP思想为主线,在其二次规划(QP)子问题的求解中引入ADMM思想,将QP分解为两个相互独立的小规模QP求解.其次,借助增广拉格朗日函数和Armijo线搜索产生原始变量新迭代点.最后,以显式解析式更新对偶变量.因此,构建了一个新型ADMM-SQP算法.在较弱条件下,分析了算法通常意义下的全局收敛性,并对算法进行了初步的数值试验.