We consider a situation where each of two processors has access to a different convex function φi, 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 φ1 + φ2 is minimized, within some prespecified accuracy ε. Our objective is to determine protocols under which the number of exchanged messages is minimized.
Bibliographical noteFunding Information:
* Research supported by the Army Research Office under Contract DAAAG-29-84-K-0005 and by the OtTice of Naval Research under Contract NOOO14-84-K-0519(N R 649-003). A preliminary version of this paper was presented at the 25th IEEE Conference on Decision and Control, Athens, Greece, Dec. 1986.