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The problem can be written as (17).
This optimisation problem can be written as (39).
Then, the firm's problem can be written as follows: Ma x ( X ) Π s.t.
The joint utility-based power control and receive beamforming problem can be written as follows.
The decision making problem can be written as max q, h E [ U | s ], (3).
Then, the firm's problem can be written as follows: max X Π ( t ) s.t.
First note that this problem can be written as a power control problem because (6).
This problem can be written as: Max q 0 T = Max f ( q g ) (5).
The continuum problem can be written as an operator equation where the operator is self adjoint and positive definite.
Our optimal control problem can be written as the following abstract static optimisation problem in a Banach space: (3.7).
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The resulting convex optimization problems can be written in terms of linear matrix inequalities and sum of squares conditions for which efficient solvers exist.
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