相关论文: The Closest Point Heat Method for Solving Eikonal …

There are many numerical methods for solving partial different equations (PDEs) on manifolds such as classical implicit, finite difference, finite element, and isogeometric analysis methods which aim at improving the interoperability…

In this paper, we use Proximal Cubic regularized Newton Methods (PCNM) to optimize the sum of a smooth convex function and a non-smooth convex function, where we use inexact gradient and Hessian, and an inexact subsolver for the cubic…

We consider a scalar objective minimization problem over the solution set of another optimization problem. This problem is known as simple bilevel optimization problem and has drawn a significant attention in the last few years. Our inner…

We consider minimizing a conic quadratic objective over a polyhedron. Such problems arise in parametric value-at-risk minimization, portfolio optimization, and robust optimization with ellipsoidal objective uncertainty; and they can be…

In this paper, we tackle the challenging problem of 3D keypoint estimation of general objects using a novel implicit representation. Previous works have demonstrated promising results for keypoint prediction through direct coordinate…

Frequently, the design of physicochemical processes requires screening of large numbers of alternative designs with complex geometries. These geometries may result in conformal meshes which introduce stability issues, significant…

The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on…

This paper presents PIQP, a high-performance toolkit for solving generic sparse quadratic programs (QP). Combining an infeasible Interior Point Method (IPM) with the Proximal Method of Multipliers (PMM), the algorithm can handle…

Integral equation based numerical methods are directly applicable to homogeneous elliptic PDEs, and offer the ability to solve these with high accuracy and speed on complex domains. In this paper, extensions to problems with inhomogeneous…

Quasi-equilibrium approximation is a widely used closure approximation approach for model reduction with applications in complex fluids, materials science, etc. It is based on the maximum entropy principle and leads to thermodynamically…

As phase-field modeling (PFM) is booming across various disciplines and has been proven fitted for numerically modeling interfacial problems, we aim at taking a step back to revisit its fundamental validity, in the light of non-equilibrium…

This paper introduces a new method for solving the planar heat equation based on the Lightning Method. The lightning method is a recent development in the numerical solution of linear PDEs which expresses solutions using sums of polynomials…

Robust optimization provides a principled and unified framework to model many problems in modern operations research and computer science applications, such as risk measures minimization and adversarially robust machine learning. To use a…

In this paper, we propose new proximal Newton-type methods for convex optimization problems in composite form. The applications include model predictive control (MPC) and embedded MPC. Our new methods are computationally attractive since…

In this paper, we introduce a method for computing rigorous local inclusions of solutions of Cauchy problems for nonlinear heat equations for complex time values. Using a solution map operator, we construct a simplified Newton operator and…

This paper applies the Recursive Projection Method (RPM) to the problem of finding the effective mechanical response of a periodic heterogeneous solid. Previous works apply the Fast Fourier Transform (FFT) in combination with various…

Solving constrained nonlinear programs (NLPs) is of great importance in various domains such as power systems, robotics, and wireless communication networks. One widely used approach for addressing NLPs is the interior point method (IPM).…

Active contour models have been widely used in image segmentation, and the level set method (LSM) is the most popular approach for solving the models, via implicitly representing the contour by a level set function. However, the LSM suffers…

A numerical method using implicit surface representations is proposed to solve the linearized Poisson-Boltzmann equations that arise in mathematical models for the electrostatics of molecules in solvent. The proposed method used an implicit…

We develop a geometric version of the circle method and use it to compute the compactly supported cohomology of the space of rational curves through a point on a smooth affine hypersurface of sufficiently low degree.