Cold-start-approach: Each problem is solved independently from the next, for example, a bunch of logistic regression problems are computed in order to find the best regularization parameter λ. This can be efficient when multiple processors are used as the problems can be solved simultaneously.
Warm-start-approach: Each problem is solved using previously computed data as the starting point for the next computation. It can be done efficiently with a single processor as the problems are solved more sequentially.