  In this paper, we proposed an alternating projection based algorithm to solve
a class of distributed MIN-MAX convex optimization problems. We firstly
transform this MINMAX problem into the problem of searching for the minimum
distance between some hyper-plane and the intersection of the epigraphs of
convex functions. The Bregman's alternating method is employed in our algorithm
to achieve the distance by iteratively projecting onto the hyper-plane and the
intersection. The projection onto the intersection is obtained by cyclic
Dykstra's projection method. We further apply our algorithm to the minimum time
multi-agent consensus problem. The attainable states set for the agent can be
transformed into the epigraph of some convex functions, and the search for
time-optimal state for consensus satisfies the MIN-MAX problem formulation.
Finally, the numerous simulation proves the validity of our algorithm.
