  In this paper, we consider linear quadratic team problems with an arbitrary
number of quadratic constraints in both stochastic and deterministic settings.
The team consists of players with different measurements about the state of
nature. The objective of the team is to minimize a quadratic cost subject to
additional finite number of quadratic constraints. We first consider the
problem of countably infinite number of players in the team for a bounded state
of nature with a Gaussian distribution and show that linear decisions are
optimal. Then, we consider the problem of team decision problems with
additional convex quadratic constraints and show that linear decisions are
optimal for both the finite and infinite number of players in the team. For the
finite player case, the optimal linear decisions can be found by solving a
semidefinite program. Finally, we consider the problem of minimizing a
quadratic objective for the worst case scenario, subject to an arbitrary number
of deterministic quadratic constraints. We show that linear decisions are
optimal and can be found by solving a semidefinite program. Finally, we apply
the developed theory on dynamic team decision problems in linear quadratic
settings.
