Multiple Start Branch and Prune Filtering Algorithm for Nonconvex Optimization

Abstract

Automatic control systems, electronic circuit design, image registration, SLAM and several other engineering problems all require nonconvex optimization. Many approaches have been developed to carry out such nonconvex optimization, but they suffer drawbacks including large computation time, require tuning of multiple unintuitive parameters and are unable to find multiple local/global minima. In this work we introduce multiple start branch and prune filtering algorithm (MSBP), a Kalman filtering-based method for solving nonconvex optimization problems. MSBP starts off with a number of initial state estimates, which are branched and pruned based on the state uncertainty and innovation respectively. We show that compared to popular methods used for solving nonconvex optimization problems, MSBP has fewer parameters to tune, making it easier to use. Through a case study of point set registration, we demonstrate the efficiency of MSBP in estimating multiple global minima, and show that MSBP is robust to initial estimation error in the presence of noise and incomplete data. The results are compared to other popular methods for nonconvex optimization using standard datasets. Overall MSBP offers a better success rate at finding the optimal solution with less computation time.