A Newton algorithm for semi-discrete optimal transport with storage fees

Computational Semi-Discrete Optimal Transport with General Storage Fees

We propose and analyze a modified damped Newton algorithm to solve the semi-discrete optimal transport with storage fees. We prove global linear convergence for a wide range of storage fee functions, the main assumption being that each warehouse's storage costs are independent. We show that if $F$ is an arbitrary storage fee function that satisfies this independence condition then $F$ can be perturbed into a new storage fee function so that our algorithm converges. We also show that the optimizers are stable under these perturbations. Furthermore, our results come with quantitative rates.

多元牛顿插值在下闭空间中达到Bos--Levenberg--Trefethen函数的最优几何逼近率

Multivariate Newton Interpolation in Downward Closed Spaces Reaches the Optimal Geometric Approximation Rates for Bos--Levenberg--Trefethen Functions

将牛顿插值推广到多维下闭空间，保持二次时间与线性存储，用Leja节点实现最优几何逼近率并缓解维数灾难。

气相出现与消失作为带有互补约束的问题

Gas phase appearance and disappearance as a problem with complementarity constraints

本文针对地下核废料储存中氢气迁移的建模问题，采用Newton-min方法求解带有非线性互补约束的偏微分方程组，并验证了该方法的二次收敛性。

Approximate Linearization of Fixed Point Iterations: Error Analysis of Tangent and Adjoint Problems Linearized about Non-Stationary Points

Previous papers have shown the impact of partial convergence of discretized PDE on the accuracy of tangent and adjoint linearizations. A series of papers suggested linearization of the fixed point iteration used in the solution process as a means of computing the sensitivities rather than linearizing the discretized PDE, as the lack of convergence of the nonlinear problem indicates that the discretized form of the governing equations has not been satisfied. These works showed that the accuracy of an approximate linearization depends in part on the convergence of the nonlinear system. This work…

递归算法计算Birkhoff插值多项式

Recursive algorithms for computing Birkhoff interpolation polynomials

本文提出递归算法用于计算Birkhoff插值多项式，通过Schur补和Sylvester恒等式扩展GRPIA，减少计算成本和存储需求。

基于精确增广拉格朗日与随机迭代草图法的约束优化

Constrained Optimization via Exact Augmented Lagrangian and Randomized Iterative Sketching

本文针对等式约束非线性非凸优化问题，提出一种结合随机迭代草图求解器与精确增广拉格朗日线搜索的自适应非精确牛顿法，实现全局几乎必然收敛及局部超线性收敛，并在多个基准问题上验证了其优越性能。