Related papers: Optimization algorithms for the solution of the fr…
In this work we are interested in the construction of numerical methods for high dimensional constrained nonlinear optimization problems by particle-based gradient-free techniques. A consensus-based optimization (CBO) approach combined with…
We consider meshless approximation for solutions of boundary value problems (BVPs) of elliptic Partial Differential Equations (PDEs) via symmetric kernel collocation. We discuss the importance of the choice of the collocation points, in…
For the binary classification problem, a novel nonlinear kernel-free quadratic hyper-surface support vector machine with 0-1 loss function (QSSVM$_{0/1}$) is proposed. Specifically, the task of QSSVM$_{0/1}$ is to seek a quadratic…
We propose a boundary neuron method with random features (BNM-RF) for solving partial differential equations. The method approximates the unknown boundary function by a shallow network within the boundary integral formulation. With randomly…
We develop mathematical models for shape design and topology optimization in structural contact problems involving friction between elastic and rigid bodies. The governing mechanical constraint is a nonlinear, non-smooth, and non-convex…
The ultimate goal of any numerical scheme for partial differential equations (PDEs) is to compute an approximation of user-prescribed accuracy at quasi-minimal computational time. To this end, algorithmically, the standard adaptive finite…
A surface integral representation of Maxwell's equations allows the efficient electromagnetic (EM) modeling of three-dimensional structures with a two-dimensional discretization, via the boundary element method (BEM). However, existing BEM…
We begin by addressing the time-domain full-waveform inversion using the adjoint method. Next, we derive the scaled boundary semi-weak form of the scalar wave equation in heterogeneous media through the Galerkin method. Unlike conventional…
Recently, minimax optimization received renewed focus due to modern applications in machine learning, robust optimization, and reinforcement learning. The scale of these applications naturally leads to the use of first-order methods.…
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…
Many practitioners who use the EM algorithm complain that it is sometimes slow. When does this happen, and what can be done about it? In this paper, we study the general class of bound optimization algorithms - including…
We consider the least-squares finite element method (lsfem) for systems of nonlinear ordinary differential equations and establish an optimal error estimate for this method when piecewise linear elements are used. The main assumptions are…
Performance analysis of first-order algorithms with inexact oracles has gained recent attention due to various emerging applications in which obtaining exact gradients is impossible or computationally expensive. Previous research has…
Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint…
An efficient method is presented for solving axisymmetric, frictionless contact problems between a rigid punch and an elastically non-homogeneous, power-law graded half-space. Provided that the contact area is simply-connected profiles of…
In this work we consider the hybrid Data-Driven Computational Mechanics (DDCM) approach, in which a smooth constitutive manifold is reconstructed to obtain a well-behaved nonlinear optimization problem (NLP) rather than the much harder…
We consider a class of distributed optimization problem where the objective function consists of a sum of strongly convex and smooth functions and a (possibly nonsmooth) convex regularizer. A multi-agent network is assumed, where each agent…
The Poisson-Boltzmann equation is widely used to model molecular electrostatics; however, it is usually solved in linearised form because the sinh nonlinearity is challenging, limiting its applicability in highly charged systems such as…
This article proposes a hybrid adaptive numerical method based on the Dual Reciprocity Method (DRM) to solve problems with non-linear boundary conditions and large-scale problems, named Hybrid Adaptive Dual Reciprocity Method (H-DRM). The…
In this paper, we are interested in finding the global minimizer of a nonsmooth nonconvex unconstrained optimization problem. By combining the discrete consensus-based optimization (CBO) algorithm and the gradient descent method, we develop…