  In this article, we derive multiple polylogarithms from multiple zeta values
by using a recursive Riemann-Hilbert problem of additive type. Furthermore we
show that this Riemann-Hilbert problem is regarded as an inverse problem for
the connection problem of the KZ equation of one variable, so that the
fundamental solutions to the equation are derived from the Drinfel'd associator
by using a Riemann-Hilbert problem of multiplicative type. These results say
that the duality relation for the Drinfel'd associator can be interpreted as
the solvability condition for this inverse problem.
