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A mathematical framework for a duplex multiple-input-multiple-output, multipoint network is presented and used to develop uplink and downlink network objective functions based on information theoretic "waterfilling" capacity arguments. It is shown that these objective functions possess equal local optima in reciprocal networks where the internode channel responses between uplink and downlink reception nodes are reciprocal, e.g., in time-division duplex networks. This mathematical framework can be used to develop locally enabled global optimization algorithms that use only local information available at each transceiver. A numerical experiment reveals an order-of-magnitude capacity improvement over conventional single-antenna systems, and/or a several-orders-of-magnitude improvement in required transmission power.