Multi-Objective Linear Quadratic Team Optimization

TL;DR

This paper addresses multi-objective linear quadratic team problems with multiple constraints in stochastic and deterministic settings, providing solutions via semidefinite programming for optimal linear decisions.

Contribution

It extends linear quadratic team optimization to include multiple quadratic constraints in both stochastic and deterministic cases, with solutions based on semidefinite programming.

Findings

Linear decisions are optimal in Gaussian cases.

Optimal solutions can be obtained through semidefinite programming.

The approach applies to worst-case deterministic scenarios.

Abstract

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.