  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 Ruszczy\'{n}ski. Moreover, we are able to derive novel enhancements
and generalizations of these well known 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 {\tt 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.
