Optimal Ergodic Control of Linear Stochastic Differential Equations with Quadratic Cost Functionals Having Indefinite Weights

Halpern加速的带退化预条件的最优非遍历收敛的majorized ADMM

Halpern-Accelerated Majorized ADMM with Optimal Non-Ergodic Convergence under Degenerate Preconditioning

本文提出一种Halpern加速的majorized ADMM，允许不定近端项，在退化预条件下实现最优非遍历收敛，并通过数值实验验证其残差衰减与优势。

Analytical and numerical solutions to ergodic control problems arising in environmental management

Environmental management optimizing a long-run objective is an ergodic control problem whose resolution can be achieved by solving an associated non-local Hamilton-Jacobi-Bellman (HJB) equation having an effective Hamiltonian. Focusing on sediment storage management as a modern engineering problem, we formulate, analyze, and compute a new ergodic control problem under discrete observations: a simple but non-trivial mathematical problem. We give optimality and comparison results of the corresponding HJB equation having unique non-smoothness and discontinuity. To numerically compute HJB equation…

Linear quadratic mean field social optimization: Asymptotic solvability and decentralized control

This paper studies asymptotic solvability of a linear quadratic (LQ) mean field social optimization problem with controlled diffusions and indefinite state and control weights. Starting with an $N$-agent model, we employ a rescaling approach to derive a low-dimensional Riccati ordinary differential equation (ODE) system, which characterizes a necessary and sufficient condition for asymptotic solvability. The decentralized control obtained from the mean field limit ensures a bounded optimality loss in minimizing the social cost having magnitude $O(N)$, which implies an optimality loss of $O(1/N…

A variational formula for risk-sensitive control of diffusions in $\mathbb{R}^d$

We address the variational problem for the generalized principal eigenvalue on $\mathbb{R}^d$ of linear and semilinear elliptic operators associated with nondegenerate diffusions controlled through the drift. We establish the Collatz-Wielandt formula for potentials that vanish at infinity under minimal hypotheses, and also for general potentials under blanket geometric ergodicity assumptions. We also present associated results having the flavor of a refined maximum principle.