Static team problems--Part I: Sufficient conditions and the exponential cost criterion

The stationary conditions of Radner are shown under relaxed hypotheses to be sufficient to establish the global optimality of candidate control laws for static team problems with convex cost. This extension of Radner's theorem establishes the optimality of affine laws for the exponential of a quadratic performance index with jointly Gaussian state and observation variables. The class of performance indexes of team problems for which the optimal solution is known is thereby enlarged.