We consider a situation where each of two processors has access to a different convex functionA, i = 1,2, defined on a common bounded domain. The processors are to exchange a number of binary messages, according to some protocol, until they find a point in the domain at which f, + h is minimized, within some prespecified accuracy E. Our objective is to determine protocols under which the number of exchanged messages is minimized. 0 1987 Academic Press. Inc.