Abstract: Firstly, the linear convergence of sequential minimal optimization (SMO) algorithm for solving the weighted minimum enclosing ball (WMEB) problem was established. Secondly, by incorporating the idea of column generation algorithm into the SMO algorithm, we proposed a column generation algorithm for solving the WMEB problem. The algorithm added the furthest point of weighted distance from the current ball center to  the core set at each iteration. The results of numerical experiments show that the proposed algorithm can effectively improve the computational efficiency of solving the WMEB problem on large
scale data sets.

Key words: weighted minimum enclosing ball (WMEB), linear convergence,  , column generation algorithm, largescale data set