  We present a new mixed integer formulation for the discrete informative path
planning problem in random fields. The objective is to compute a budget
constrained path while collecting measurements whose linear estimate results in
minimum error over a finite set of prediction locations. The problem is known
to be NP-hard. However, we strive to compute optimal solutions by leveraging
advances in mixed integer optimization. Our approach is based on expanding the
search space so we optimize not only over the collected measurement subset, but
also over the class of all linear estimators. This allows us to formulate a
mixed integer quadratic program that is convex in the continuous variables. The
formulations are general and are not restricted to any covariance structure of
the field. In simulations, we demonstrate the effectiveness of our approach
over previous branch and bound algorithms.
