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Hamilton-Jacobi Reachability for Viability Analysis of Constrained Waste-to-Energy Systems under Adversarial Uncertainty
Achraf Bouhmady, Othman Cherkaoui Dekkaki
https://arxiv.org/abs/2510.11396

Hamilton-Jacobi Reachability for Viability Analysis of Constrained Waste-to-Energy Systems under Adversarial Uncertainty
This paper investigates the problem of maintaining the safe operation of Waste-to-Energy (WtE) systems under operational constraints and uncertain waste inflows. We model this as a robust viability problem, formulated as a zero-sum differential game between a control policy and an adversarial disturbance. Within a Hamilton-Jacobi framework, the viability kernel is characterized as the zero sublevel set of a value function satisfying a constrained Hamilton-Jacobi-Bellman (HJB) equation in the vi…

Error estimates for finite-dimensional approximations of Hamilton-Jacobi-Bellman equations on the Wasserstein space
Samuel Daudin, Joe Jackson, Benjamin Seeger
https://arxiv.org/abs/2510.02652

Error estimates for finite-dimensional approximations of Hamilton-Jacobi-Bellman equations on the Wasserstein space
In this paper, we study a Hamilton-Jacobi-Bellman (HJB) equation set on the Wasserstein space $\mathcal{P}_2(\mathbb{R}^d)$, with a second order term arising from a purely common noise. We do not assume that the Hamiltonian is convex in the momentum variable, which means that we cannot rely on representation formulas coming from mean field control. In this setting, Gangbo, Mayorga, and Święch showed via viscosity solutions methods that the HJB equation on $\mathcal{P}_2(\mathbb{R}^d)$ can be …

Hamilton--Jacobi--Bellman equation for optimal control of stochastic Wasserstein--Hamiltonian system on graphs
Jianbo Cui, Tonghe Dang
https://arxiv.org/abs/2509.25965 https://

Hamilton--Jacobi--Bellman equation for optimal control of stochastic Wasserstein--Hamiltonian system on graphs
Stochastic optimal control problems for Hamiltonian dynamics on graphs have wide-ranging applications in mechanics and quantum field theory, particularly in systems with graph-based structures. In this paper, we establish the existence and uniqueness of viscosity solutions for a new class of Hamilton--Jacobi--Bellman (HJB) equations arising from the optimal control of stochastic Wasserstein--Hamiltonian systems (SWHSs) on graphs. One distinctive feature of these HJB equations is the simultaneou…

Analysis of approximate linear programming solution to Markov decision problem with log barrier function
Donghwan Lee, Hyukjun Yang, Bum Geun Park
https://arxiv.org/abs/2509.19800

Analysis of approximate linear programming solution to Markov decision problem with log barrier function
There are two primary approaches to solving Markov decision problems (MDPs): dynamic programming based on the Bellman equation and linear programming (LP). Dynamic programming methods are the most widely used and form the foundation of both classical and modern reinforcement learning (RL). By contrast, LP-based methods have been less commonly employed, although they have recently gained attention in contexts such as offline RL. The relative underuse of the LP-based methods stems from the fact t…

A semi-Lagrangian method for solving state constraint Mean Field Games in Macroeconomics
Fabio Camilli, Qing Tang, Yong-shen Zhou
https://arxiv.org/abs/2510.00768 https://

A semi-Lagrangian method for solving state constraint Mean Field Games in Macroeconomics
We study continuous-time heterogeneous agent models cast as Mean Field Games, in the Aiyagari-Bewley-Huggett framework. The model couples a Hamilton-Jacobi-Bellman equation for individual optimization with a Fokker-Planck-Kolmogorov equation for the wealth distribution. We establish a comparison principle for constrained viscosity solutions of the HJB equation and propose a semi-Lagrangian (SL) scheme for its numerical solution, proving convergence via the Barles-Souganidis method. A policy ite…

Analysis of approximate linear programming solution to Markov decision problem with log barrier function
Donghwan Lee, Hyukjun Yang, Bum Geun Park
https://arxiv.org/abs/2509.19800

Analysis of approximate linear programming solution to Markov decision problem with log barrier function
There are two primary approaches to solving Markov decision problems (MDPs): dynamic programming based on the Bellman equation and linear programming (LP). Dynamic programming methods are the most widely used and form the foundation of both classical and modern reinforcement learning (RL). By contrast, LP-based methods have been less commonly employed, although they have recently gained attention in contexts such as offline RL. The relative underuse of the LP-based methods stems from the fact t…

Optimal Consumption-Investment with Epstein-Zin Utility under Leverage Constraint
Dejian Tian, Weidong Tian, Jianjun Zhou, Zimu Zhu
https://arxiv.org/abs/2509.21929 https://

Optimal Consumption-Investment with Epstein-Zin Utility under Leverage Constraint
We study optimal portfolio choice under Epstein-Zin recursive utility in the presence of general leverage constraints. We first establish that the optimal value function is the unique viscosity solution to the associated Hamilton-Jacobi-Bellman (HJB) equation, by developing a new dynamic programming principle under constraints. We further demonstrate that the value function admits smoothness and characterize the optimal consumption and investment strategies. In addition, we derive explicit solu…

Crosslisted article(s) found for math.AP. https://arxiv.org/list/math.AP/new
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- Hamilton--Jacobi--Bellman equation for optimal control of stochastic Wasserstein--Hamiltonian sys...
Jianbo Cui, Tonghe Dang