Appendix A Convergence Analysis

Hence, we prove the convergence in a finite manner. Lemma 4. The bounding operation in Algorithm 1 is finitely consistent. From Lemma 4, we have the bounding operation in Algorithm 1 is finitely consistent. Theorem 1. Algorithm 1 is convergent to the global optimal solution after a finite step From Lemma 6, we have Algorithm 1 terminates after finite steps. After bound tightening according to the "medoids on samples" constraint, Consequently, we have proved Theorem 1. 14 B Parallel results of large scale datasets Table 5 shows the parallel numerical results for large scale datasets with 10,000 to 2,458,285 samples.