  We investigate an optimization problem of finding quantum sequential
measurements, which forms a wide class of state discrimination problems with
the restriction that only sequential measurements are allowed. Sequential
measurements from Alice to Bob on a bipartite system are considered. Using the
fact that the optimization problem can be formulated as a problem with only
Alice's measurement and is convex programming, we derive its dual problem and
necessary and sufficient conditions for an optimal solution. In the problem we
address, the output of Alice's measurement can be infinite or continuous, while
sequential measurements with a finite number of outcomes are considered. It is
shown that there exists an optimal sequential measurement in which Alice's
measurement with a finite number of outcomes as long as a solution exists. We
also show that if the problem has a certain symmetry, then there exists an
optimal solution with the same type of symmetry. A minimax version of the
problem is considered, and necessary and sufficient conditions for a minimax
solution are derived. An example in which our results can be used to obtain an
analytical expression for an optimal sequential measurement is finally
provided.
