This article presents BiqCrunch , an exact solver for binary quadratic optimization problems. BiqCrunch is a branch-and-bound method that uses an original, efficient semidefinite-optimization-based bounding procedure. It has been successfully tested on a variety of well-known combinatorial optimization problems, such as Max-Cut, Max- k -Cluster, and Max-Independent-Set. The code is publicly available online; a web interface and many conversion tools are also provided.

We present a method to estimate a positive semidefinite matrix by linear least squares, and we apply this method to the estimation of local compliance matrices during deformable object modeling. Estimation of physical quantities from measurements has to consider noise due to measurement and modeling inaccuracy. Enforcing constraints during estimation can guarantee physically plausible results even under difficult measurement conditions.