We study the problem of computing the capacity of a discrete memoryless
channel under uncertainty affecting the channel law matrix, and possibly with a
constraint on the average cost of the input distribution. The problem has been
formulated in the literature as a max-min problem. We use the robust
optimization methodology to convert the max-min problem to a standard convex
optimization problem. For small-sized problems, and for many types of
uncertainty, such a problem can be solved in principle using interior point
methods (IPM). However, for large-scale problems, IPM are not practical. Here,
we suggest an O(1/T) first-order algorithm based on Nemirovski
(2004) which is applied directly to the max-min problem.Comment: 22 pages, 2 figure