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arXiv · 1801.02306

Linear-Quadratic Mean Field Control: The Hamiltonian Matrix and Invariant Subspace Method

Xiang Chen·Minyi Huang
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Abstract

This paper studies the existence and uniqueness of a solution to linear quadratic (LQ) mean field social optimization problems with uniform agents. We exploit a Hamiltonian matrix structure of the associated ordinary differential equation (ODE) system and apply a subspace decomposition method to find the solution. This approach is effective for both the existence analysis and numerical computations. We further extend the decomposition method to LQ mean field games.

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Xiang Chen, Minyi Huang. 2018-01-08. Linear-Quadratic Mean Field Control: The Hamiltonian Matrix and Invariant Subspace Method. https://arxiv.org/abs/1801.02306

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