A semi-proximal augmented Lagrangian based decomposition method for primal block angular convex composite quadratic conic programming problems [article]

Xin-Yee Lam, Defeng Sun, Kim-Chuan Toh
2018 arXiv   pre-print
We propose a semi-proximal augmented Lagrangian based decomposition method for convex composite quadratic conic programming problems with primal block angular structures. Using our algorithmic framework, we are able to naturally derive several well known augmented Lagrangian based decomposition methods for stochastic programming such as the diagonal quadratic approximation method of Mulvey and Ruszczyński. Moreover, we are able to derive novel enhancements and generalizations of these well
more » ... methods. We also propose a semi-proximal symmetric Gauss-Seidel based alternating direction method of multipliers for solving the corresponding dual problem. Numerical results show that our algorithms can perform well even for very large instances of primal block angular convex QP problems. For example, one instance with more than 300,000 linear constraints and 12,500,000 nonnegative variables is solved in less than a minute whereas Gurobi took more than 3 hours, and another instance qp-gridgen1 with more than 331,000 linear constraints and 986,000 nonnegative variables is solved in about 5 minutes whereas Gurobi took more than 35 minutes.
arXiv:1812.04941v1 fatcat:jjah6n7onrd6xihrzr7pvrofua