Related papers: The Closest Point Method for Surface PDEs with Gen…
In this work, we focus on the Neumann-Neumann method (NNM), which is one of the most popular non-overlapping domain decomposition methods. Even though the NNM is widely used and proves itself very efficient when applied to discrete problems…
This paper presents a directional proximal point method (DPPM) to derive the minimum of any C1-smooth function f. The proposed method requires a function persistent a local convex segment along the descent direction at any non-critical…
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…
A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential…
This paper presents a particle-based optimization method designed for addressing minimization problems with equality constraints, particularly in cases where the loss function exhibits non-differentiability or non-convexity. The proposed…
The solution of partial differential equations (PDEs) on complex domains often presents a significant computational challenge by requiring the generation of fitted meshes. The Diffuse Domain Method (DDM) is an alternative which reformulates…
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…
The solution of the elliptic partial differential equation has interface singularity at the points which are either the intersections of interfaces or the intersections of interfaces with the boundary of the domain. The singularities that…
In this paper we generalize the Interior Point-Proximal Method of Multipliers (IP-PMM) presented in [An Interior Point-Proximal Method of Multipliers for Convex Quadratic Programming, Computational Optimization and Applications, 78,…
We show strong uniform convergence of monotone P1 finite element methods to the viscosity solution of isotropic parabolic Hamilton-Jacobi-Bellman equations with mixed boundary conditions on unstructured meshes and for possibly degenerate…
This paper presents a comprehensive analysis of a broad range of variations of the stochastic proximal point method (SPPM). Proximal point methods have attracted considerable interest owing to their numerical stability and robustness…
We consider prescribed mean curvature equations whose solutions are minimal surfaces, constant mean curvature surfaces, or capillary surfaces. We consider both Dirichlet boundary conditions for Plateau problems and nonlinear Neumann…
This paper is part of a series developing $C^0$ finite element methods for fourth-order elliptic equations on polygonal domains. Here, we investigate how boundary conditions influence the design of effective $C^0$ schemes, specifically…
In this paper, we propose a numerical method to approximate the solution of partial differential equations in irregular domains with no-flux boundary conditions by means of spectral methods. The main features of this method are its…
We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…
Employing the ideas of non-linear preconditioning and testing of the classical proximal point method, we formalise common arguments in convergence rate and convergence proofs of optimisation methods to the verification of a simple…
Particle-based methods are a practical tool in computational fluid dynamics, and novel types of methods have been proposed. However, widely developed Lagrangian-type formulations suffer from the nonuniform distribution of particles, which…
The recent development of spectral method has been praised for its high-order convergence in simulating complex physical problems. The combination of embedded boundary method and spectral method becomes a mainstream way to tackle…
We consider optimization problems over the Stiefel manifold whose objective function is the summation of a smooth function and a nonsmooth function. Existing methods for solving this kind of problems can be classified into three classes.…
This paper proposes a Riemannian Multiobjective Proximal Gradient Method (RMPGM) for composite optimization problems on manifolds. Unlike scalarization-based approaches, the proposed framework directly handles vector-valued objectives and…