  This work develops a distributed optimization strategy with guaranteed exact
convergence for a broad class of left-stochastic combination policies. The
resulting exact diffusion strategy is shown in Part II to have a wider
stability range and superior convergence performance than the EXTRA strategy.
The exact diffusion solution is applicable to non-symmetric left-stochastic
combination matrices, while many earlier developments on exact consensus
implementations are limited to doubly-stochastic matrices; these latter
matrices impose stringent constraints on the network topology. The derivation
of the exact diffusion strategy in this work relies on reformulating the
aggregate optimization problem as a penalized problem and resorting to a
diagonally-weighted incremental construction. Detailed stability and
convergence analyses are pursued in Part II and are facilitated by examining
the evolution of the error dynamics in a transformed domain. Numerical
simulations illustrate the theoretical conclusions.
