arXiv subjects

Youyicun Lin

Publications and source records attributed to Youyicun Lin.

3 recordsLinked to original sources

arXiv2025

An Efficient Augmented Lagrangian Framework for Dynamic Optimal Transport on Surfaces Based on Second-Order Cone Programming Reformulation

This paper proposes an efficient numerical optimization framework for solving dynamic optimal transport (DOT) problems on surfaces, computing both the quadratic Wasserstein distance and the associated interpolation. Building on the convex DOT model of Benamou-Brenier-Lisini, we first properly reformulate its dual problem, discretized on a triangular mesh in space and a staggered grid in time, into a linear second-order cone programming (SOCP) problem. Then the resulting SOCP is solved via an inexact proximal augmented Lagrangian method with a highly efficient numerical implementation, and the algorithm is guaranteed to converge to a Karush-Kuhn-Tucker point without imposing any additional assumptions. Finally, we implement the proposed framework as an open-source software package. The effectiveness, robustness, and computational efficiency of the software are validated through extensive numerical experiments across diverse datasets, demonstrating that it consistently outperforms state-of-the-art surface DOT solvers by several times in speed, while the commercial solvers Gurobi and MOSEK either fail to solve the same SOCP reformulation due to out-of-memory or require substantially prolonged computation times.

math.OC↗

arXiv2025

A Convergent Inexact Abedin-Kitagawa Iteration Method for Monge-Amp\`ere Eigenvalue Problems

This paper proposes an inexact Aleksandrov-solution-based iteration method, formulated by adapting the convergent Rayleigh inverse iterative scheme introduced by Abedin and Kitagawa, to solve real Monge-Amp{\`e}re eigenvalue (MAE) problems. The central feature of the proposed approach is the introduction of a flexible error tolerance criterion for computing inexact Aleksandrov solutions to the required subproblems. This allows the inner iteration to be solved approximately without compromising the global convergence properties of the overall scheme, as we established under a ${\cal C}^{2,\alpha}$ boundary condition, and has the potential of achieving reduced computational cost compared to the original algorithm. In practice, for both two- and three-dimensional problems, by leveraging the flexibility of the inexact iterative formulation in conjunction with a fixed-point approach for solving the subproblems, the proposed method performs several times faster than its original version of Abedin and Kitagawa, across all tested problem instances in the numerical experiments.

math.NA↗

arXiv2025

An efficient second-order cone programming approach for dynamic optimal transport on staggered grid discretization

This paper proposes an efficient numerical method based on second-order cone programming (SOCP) to solve dynamic optimal transport (DOT) problems with quadratic cost on staggered grid discretization. By properly reformulating discretized DOT problems into a linear SOCP, the proposed method eliminates the interpolation matrices and thus avoids solving a series of cubic equations and linear systems induced by interpolation. Then, by taking advantage of the SOCP reformulation, we can solve them efficiently by a computationally highly economical implementation of an inexact decomposition-based proximal augmented Lagrangian method. Moreover, we have made the proposed approach an open-source software package. Numerical experiments on various DOT problems suggest that the proposed approach performs significantly more efficiently than state-of-the-art software packages. In addition, it exhibits prominent robustness to problems with non-negative measures.

math.OC↗