  A bipartite bilinear program (BBP) is a quadratically constrained quadratic
optimization problem where the variables can be partitioned into two sets such
that fixing the variables in any one of the sets results in a linear program.
We propose a new second order cone representable (SOCP) relaxation for BBP,
which we show is stronger than the standard SDP relaxation intersected with the
boolean quadratic polytope. We then propose a new branching rule inspired by
the construction of the SOCP relaxation. We describe a new application of BBP
called as the finite element model updating problem, which is a fundamental
problem in structural engineering. Our computational experiments on this
problem class show that the new branching rule together with an polyhedral
outer approximation of the SOCP relaxation outperforms a state-of-the-art
commercial global solver in obtaining dual bounds.
