  Multi-user Gaussian MIMO wiretap channel is considered under interference
power constraints (IPC), in addition to the total transmit power constraint
(TPC). Algorithms for \textit{global} maximization of its secrecy rate are
proposed. Their convergence to the secrecy capacity is rigorously proved and a
number of properties are established analytically. Unlike known algorithms, the
proposed ones are not limited to the MISO case and are proved to converge to a
\textit{global} rather than local optimum in the general MIMO case, even when
the channel is not degraded. In practice, the convergence is fast as only a
small to moderate number of Newton steps is required to achieve a high
precision level. The interplay of TPC and IPC is shown to result in an unusual
property when an optimal point of the max-min problem does not provide an
optimal transmit covariance matrix in some (singular) cases. To address this
issue, an algorithm is developed to compute an optimal transmit covariance
matrix in those singular cases. It is shown that this algorithm also solves the
dual (nonconvex) problems of \textit{globally} minimizing the total transmit
power subject to the secrecy and interference constraints; it provides the
minimum transmit power and respective signaling strategy needed to achieve the
secrecy capacity, hence allowing power savings.
