  We propose the novel p-branch-and-bound method for solving two-stage
stochastic programming problems whose deterministic equivalents are represented
by non-convex mixed-integer quadratically constrained quadratic programming
(MIQCQP) models. The precision of the solution generated by the
p-branch-and-bound method can be arbitrarily adjusted by altering the value of
the precision factor p. The proposed method combines two key techniques. The
first one, named p-Lagrangian decomposition, generates a mixed-integer
relaxation of a dual problem with a separable structure for a primal non-convex
MIQCQP problem. The second one is a version of the classical dual decomposition
approach that is applied to solve the Lagrangian dual problem and ensures that
integrality and non-anticipativity conditions are met once the optimal solution
is obtained. This paper also presents a comparative analysis of the
p-branch-and-bound method efficiency considering two alternative solution
methods for the dual problems as a subroutine. These are the proximal bundle
method and Frank-Wolfe progressive hedging. The latter algorithm relies on the
interpolation of linearisation steps similar to those taken in the Frank-Wolfe
method as an inner loop in the classic progressive hedging. The
p-branch-and-bound method's efficiency was tested on randomly generated
instances and demonstrated superior performance over commercial solver Gurobi.
