Related papers: Adaptive mesh point selection for the efficient so…
When solving elliptic partial differential equations in a region containing immersed interfaces (possibly evolving in time), it is often desirable to approximate the problem using an independent background discretisation, not aligned with…
We establish the optimal nonergodic sublinear convergence rate of the proximal point algorithm for maximal monotone inclusion problems. First, the optimal bound is formulated by the performance estimation framework, resulting in an infinite…
We consider stochastic optimization problems where data is drawn from a Markov chain. Existing methods for this setting crucially rely on knowing the mixing time of the chain, which in real-world applications is usually unknown. We propose…
We propose joining a flexible mesh design with an integrated residual transcription in order to improve the accuracy of numerical solutions to optimal control problems. This approach is particularly useful when state or input trajectories…
In this paper, we consider gradient-type methods for convex positively homogeneous optimization problems with relative accuracy. An analogue of the accelerated universal gradient-type method for positively homogeneous optimization problems…
We present a one-dimensional shear-force-driven droplet formation model with a flux-based error estimator. The model is derived using asymptotic expansion and a front-tracking method to simulate the droplet interface. The model is then…
Traditional numerical techniques for solving time-dependent partial-differential-equation (PDE) initial-value problems (IVPs) store a truncated representation of the function values and some number of their time derivatives at each time…
In this paper, we obtain global $\mathcal{O} (1/ \sqrt{k})$ pointwise and $\mathcal{O} (1/ {k})$ ergodic convergence rates for a variable metric proximal alternating direction method of multipliers(VM-PADMM) for solving linearly constrained…
In the setting of high-dimensional linear models with Gaussian noise, we investigate the possibility of confidence statements connected to model selection. Although there exist numerous procedures for adaptive point estimation, the…
Non-convex optimization is a critical tool in advancing machine learning, especially for complex models like deep neural networks and support vector machines. Despite challenges such as multiple local minima and saddle points, non-convex…
In this paper, we study optimal experimental design problems with a broad class of smooth convex optimality criteria, including the classical A-, D- and p th mean criterion. In particular, we propose an interior point (IP) method for them…
Meshless methods are commonly used to determine numerical solutions to partial differential equations (PDEs) for problems involving free surfaces and/or complex geometries, approximating spatial derivatives at collocation points via local…
This paper presents the development and analysis of an asymptotically compatible (AC) unfitted finite element method for one-dimensional nonlocal elliptic interface problems. The proposed method achieves optimal error estimates through…
The adaptive Iterative Soft-Thresholding Algorithm (ISTA) has been a popular algorithm for finding a desirable solution to the LASSO problem without explicitly tuning the regularization parameter $\lambda$. Despite that the adaptive ISTA is…
We consider the problem of inverse kinematics (IK), where one wants to find the parameters of a given kinematic skeleton that best explain a set of observed 3D joint locations. The kinematic skeleton has a tree structure, where each node is…
Computing the dispersion relation for two-dimensional photonic crystals is a notoriously challenging task: It involves solving parameterized Helmholtz eigenvalue problems with high-contrast coefficients. To resolve the challenge, we propose…
An optimal mesh size of the sampling region can help to reduce computational burden in practical applications. In this work, we investigate optimal choices of mesh sizes for the identifications of medium obstacles from either the far-field…
Temporal point processes have been widely applied to model event sequence data generated by online users. In this paper, we consider the problem of how to design the optimal control policy for point processes, such that the stochastic…
One of the main challenges in numerically solving partial differential equations is finding a discretisation for the computational domain that balances the accurate representation of the underlying field with computational efficiency.…
Although adaptive optimization algorithms have been successful in many applications, there are still some mysteries in terms of convergence analysis that have not been unraveled. This paper provides a novel non-convex analysis of adaptive…