Initial point (z0) in tfocs_SCD

If I solve the same problem using tfocs_SCD repetitively while setting z0 to be the previous solution, like this:

while (true)
     [ x, out ] = tfocs_SCD( objectiveF, affineF, conjnegF, mu, x0, out.dual, opts, continuationOptions );

Will tfocs_SCD converge instantaneously?

For the test I did, it seems that although tfocs_SCD converges with less iterations than starting from scratch, it is far from instantaneous.

Would someone care to explain why?