Block Subgradient Greedy Kaczmarz Methods for Robotic Grasping Problems

The robotic grasping problem is firstly cast as a linear complementarity problem and reformulated into nonsmooth equations. We propose two block Kaczmarz methods to solve the equations. The K-means clustering algorithm is utilized to partition the nonsmooth equations. Based on the resulting block information, the subgradient greedy randomized Kaczmarz method and the subgradient multi-step greedy Kaczmarz method are constructed. Asymptotic convergence of the proposed block subgradient Kaczmarz methods is given. Numerical results confirm the superior computational accuracy of the new methods.