Abstract:

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.

Key words: linear constrained, two blocks nonconvex optimization, alternating direction method of multipliers, sequential quadratic programming method, algorithm