arXiv subjects

Thanh-Son Trinh

Publications and source records attributed to Thanh-Son Trinh.

5 recordsLinked to original sources

arXiv2025

Weak Optimal Entropy Transport Problems

In this paper, we introduce weak optimal entropy transport problems that cover both optimal entropy transport problems and weak optimal transport problems introduced by Liero, Mielke, and Savaré [27]; and Gozlan, Roberto, Samson and Tetali [20], respectively. Under some mild assumptions of entropy functionals, we establish a Kantorovich type duality for our weak optimal entropy transport problem. We also introduce martingale optimal entropy transport problems, and express them in terms of duality, homogeneous marginal perspective functionals and homogeneous constraints.

math.FA↗

arXiv2024

Modified Wasserstein gradient flow formulation of time-fractional porous medium equations with nonlocal pressure

We consider a class of time-fractional porous medium equations with nonlocal pressure. We show the existence of their weak solutions by proposing a JKO scheme for modified Wasserstein distance and a square fractional Sobolev norm. Moreover, the regularization effect and the Lp norm estimate are established in this paper.

math.AP↗

arXiv2021

Event-triggered bipartite consensus for multiagent system with general linear dynamics: an integral-type event triggered control

In this paper, we propose an integral based event-triggering controller for bipartite consensus of the multi-agent systems whose dynamics are described by general linear system. We prove that the system achieves the bipartite consensus in asymptotic regime and there is a positive minimum inter-event time (MIET) between two consecutive triggering times of each agent. The proof of the asymptotive stability involves a novel argument used to bound the norm of the difference between the true state and its estimated state (for each time) by an integration of its square. Numerical results are provided supporting the effectiveness of the proposed controller.

math.OC↗

arXiv2021

Weak optimal total variation transport problems and generalized Wasserstein barycenters

In this paper, we establish a Kantorovich duality for weak optimal total variation transport problems. As consequences, we recover a version of duality formula for partial optimal transports established by Caffarelli and McCann; and we also get another proof of Kantorovich-Rubinstein Theorem for generalized Wasserstein distance $\widetilde{W}_1^{a,b}$ proved before by Piccoli and Rossi. Then we apply our duality formula to study generalized Wasserstein barycenters. We show the existence of these barycenters for measures with compact supports. Finally, we prove the consistency of our barycenters.

math.OC↗

arXiv2019

Duality and quotient spaces of generalized Wasserstein spaces

In this article, using ideas of Liero, Mielke and Savaré in [21], we establish a Kantorovich duality for generalized Wasserstein distances $W_1^{a,b}$ on a generalized Polish metric space, introduced by Picolli and Rossi. As a consequence, we give another proof that $W_1^{a,b}$ coincide with flat metrics which is a main result of [25], and therefore we get a result of independent interest that $\left(\mathcal{M}(X), W^{a,b}_1\right)$ is a geodesic space for every Polish metric space $X$. We also prove that $(\mathcal{M}^G(X),W_p^{a,b})$ is isometric isomorphism to $(\mathcal{M}(X/G),W_p^{a,b})$ for isometric actions of a compact group $G$ on a Polish metric space $X$; and several results of Gromov-Hausdorrf convergence and equivariant Gromov-Hausdorff convergence of generalized Wasserstein spaces. The latter results were proved for standard Wasserstein spaces in [22],[14] and [8] respectively.

math.MG↗