  We propose a new approach to sequential testing which is an adaptive
(on-line) extension of the (off-line) framework developed in [10]. It relies
upon testing of pairs of hypotheses in the case where each hypothesis states
that the vector of parameters underlying the dis- tribution of observations
belongs to a convex set. The nearly optimal under appropriate conditions test
is yielded by a solution to an efficiently solvable convex optimization prob-
lem. The proposed methodology can be seen as a computationally friendly
reformulation of the classical sequential testing.
