As a typical method for solving non-smooth convex optimization problems

cutting plane method is widely used in solving support vector machine problems. However

this algorithm suffers from the instability problem. To ease this instability

researchers proposed an optimized cutting plane algorithm which incorporated a line search stage. However

the computational complexity of such algorithm is too high for applications where the number of training samples is large. In this paper we propose an active set based optimized cutting plane algorithm to reduce the computation complexity of the original algorithm. When computing the objective function and performing line search

only those samples which fall in the active set are considered. Compared to optimized cutting plane algorithm

the proposed algorithm needs to calculate the objective function and perform line search only for a small fraction of the samples

leading to a significant drop in computational complexity without losing accuracy.