Multi-Objective Linear Quadratic Team Optimization

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 will first consider the Gaussian case, where the state of nature is assumed to have a Gaussian distribution, and show that the linear decisions are optimal and can be found by solving a semidefinite program We then 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 can be found by solving a semidefinite program.