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12
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Introduction
I am currently with CERMICS, École nationale des ponts et chaussées as a postdoctoral fellow advised by Prof. Éric Cancès. I received the Bachelor degree (2019) in Mathematics and Applied Mathematics at Tongji University and the Ph.D. degree (2024) in Computational Mathematics at the University of Chinese Academy of Sciences under the supervision of Prof. Xin Liu. My research interests focus on developing numerical optimization methods for computational materials science.
Skills and Expertise
Current institution
Additional affiliations
July 2024 - August 2024
Education
September 2019 - July 2024
September 2015 - July 2019
Publications
Publications (12)
In this work, we construct a novel numerical method for solving the multi-marginal optimal transport problems with Coulomb cost. This type of optimal transport problems arises in quantum physics and plays an important role in understanding the strongly correlated quantum systems. With a Monge-like ansatz, we transfer the original high-dimensional p...
We consider solving a special class of optimal transport problems with complementarity constraints, which arise from density functional theory. Moreover, the transport maps are constrained by certain mutual exclusion rules. In this paper, we focus on the cases with two transport maps. For purposes of algorithmic design, we move the complementarity...
Tensor product function (TPF) approximations have been widely adopted in solving high-dimensional problems, such as partial differential equations and eigenvalue problems, achieving desirable accuracy with computational overhead that scales linearly with problem dimensions. However, recent studies have underscored the extraordinarily high computati...
This paper is concerned with ab initio crystal structure relaxation under a fixed unit cell volume, which is a step in calculating the static equations of state and forms the basis of thermodynamic property calculations for materials. The task can be formulated as an energy minimization with a determinant constraint. Widely used line minimization-b...
This paper focuses on multi-block optimization problems over transport polytopes, which underlie various applications including strongly correlated quantum physics and machine learning. Conventional block coordinate descent-type methods for the general multi-block problems store and operate on the matrix variables directly, resulting in formidable...
In this work, we construct a novel numerical method for solving the multimarginal optimal transport problems with Coulomb cost. This type of optimal transport problem arises in quantum physics and plays an important role in understanding the strongly correlated quantum systems. With a Monge-like ansatz, we transfer the original high-dimensional pro...
The proximal alternating linearized minimization (PALM) method suits well for solving block-structured optimization problems, which are ubiquitous in real applications. In the cases where subproblems do not have closed-form solutions, e.g., due to complex constraints, infeasible subsolvers are indispensable, giving rise to an infeasible inexact PAL...
In a Mathematical Program with Generalized Complementarity Constraints (MPGCC), complementarity relationships are imposed between each pair of variable blocks. MPGCC includes the traditional Mathematical Program with Complementarity Constraints (MPCC) as a special case. On account of the disjunctive feasible region, MPCC and MPGCC are generally dif...
The proximal alternating linearized minimization method (PALM) suits well for solving block-structured optimization problems, which are ubiquitous in real applications. In the cases where subproblems do not have closed-form solutions, e.g., due to complex constraints, infeasible subsolvers are indispensable, giving rise to an infeasible inexact PAL...
Force-based algorithms for ab initio atomic structure relaxation, such as conjugate gradient methods, usually get stuck in the line minimization processes along search directions, where expensive ab initio calculations are triggered frequently to test trial positions before locating the next iterate. We present a force-based gradient descent method...
The proximal alternating linearized minimization method (PALM) suits well for solving block-structured optimization problems, which are ubiquitous in real applications. In the cases where subproblems do not have closed-form solutions, e.g., due to complex constraints, infeasible sub-solvers are indispensable, giving rise to an infeasible inexact PA...
In this work, we construct a novel numerical method for solving the multi-marginal optimal transport problems with Coulomb cost. This type of optimal transport problems arises in quantum physics and plays an important role in understanding the strongly correlated quantum systems. With a Monge-like ansatz, we transfer the original high-dimensional p...
