  We study the maximum-confidence (MC) measurement strategy for discriminating
among nonorthogonal symmetric qudit states. Restricting to linearly dependent
and equally likely pure states, we find the optimal positive operator valued
measure (POVM) that maximizes our confidence in identifying each state in the
set and minimizes the probability of obtaining inconclusive results. The
physical realization of this POVM is completely determined and it is shown that
after an inconclusive outcome, the input states may be mapped into a new set of
equiprobable symmetric states, restricted, however, to a subspace of the
original qudit Hilbert space. By applying the MC measurement again onto this
new set, we can still gain some information about the input states, although
with less confidence than before. This leads us to introduce the concept of
"sequential maximum-confidence" (SMC) measurements, where the optimized MC
strategy is iterated in as many stages as allowed by the input set, until no
further information can be extracted from an inconclusive result. Within each
stage of this measurement our confidence in identifying the input states is the
highest possible, although it decreases from one stage to the next. In
addition, the more stages we accomplish within the maximum allowed, the higher
will be the probability of correct identification. We will discuss an explicit
example of the optimal SMC measurement applied in the discrimination among four
symmetric qutrit states and propose an optical network to implement it.
