COMPLEXITY OF CONVEX OPTIMIZATION

We consider a situation where each one of two processors has access to a different convex function fi, 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 fl + f2 is minimized, within some prespecified accuracy E. Our objective is to determine protocols under which the number of exchanged messages is minimized.