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Building upon recent works on linesearch-free adaptive proximal gradient methods, this paper proposes adaPG$^{q,r}$, a framework that unifies and extends existing results by providing larger stepsize policies and improved lower bounds.…

In the context of convex optimization problems in Hilbert spaces, we induce inertial effects into the classical ADMM numerical scheme and obtain in this way so-called inertial ADMM algorithms, the convergence properties of which we…

An adapted bubble approach which is a modifiation of the residual-free bubbles (RFB) method, is proposed for the Helmhotz problem in 2D. A new two-level finite element method is introduced for the approximations of the bubble functions.…

Iteration methods based on barycentric rational interpolation are derived that exhibit accelerating orders of convergence. For univariate root search, the derivative-free methods approach quadratic convergence and the first-derivative…

Fractal interpolation functions (FIFs) developed through iterated function systems (IFSs) prove more versatile than classical interpolants. However, the applications of FIFs in the domain of `shape preserving interpolation' are not fully…

When approximating the expectations of a functional of a solution to a stochastic differential equation, the numerical performance of deterministic quadrature methods, such as sparse grid quadrature and quasi-Monte Carlo (QMC) methods, may…

We study global optimization (GOP) in the framework of non-linear inverse problems with a unique solution. These problems are in general ill-posed. Evaluation of the objective function is often expensive, as it implies the solution of a…

Meshfree radial basis function (RBF) methods are popular tools used to numerically solve partial differential equations (PDEs). They take advantage of being flexible with respect to geometry, easy to implement in higher dimensions, and can…

This paper presents a new fast active-set quadratic programming (QP) solver based on inverse matrix updates, which is suitable for real-time model predictive control (MPC). This QP solver, called imuQP (inverse matrix update QP), is based…

This paper is concerned with convergence analysis for the mirror descent (MD) method, a well-known algorithm in convex optimization. An analysis framework via integral quadratic constraints (IQCs) is constructed to analyze the convergence…

We present two new adaptive quadrature routines. Both routines differ from previously published algorithms in many aspects, most significantly in how they represent the integrand, how they treat non-numerical values of the integrand, how…

Blind Face Restoration (BFR) addresses the challenge of reconstructing degraded low-quality (LQ) facial images into high-quality (HQ) outputs. Conventional approaches predominantly rely on learning feature representations from ground-truth…

This paper employs a policy iteration reinforcement learning (RL) method to study continuous-time linear-quadratic mean-field control problems in infinite horizon. The drift and diffusion terms in the dynamics involve the states, the…

In inverse reinforcement learning (IRL), a learning agent infers a reward function encoding the underlying task using demonstrations from experts. However, many existing IRL techniques make the often unrealistic assumption that the agent…

Constrained radial basis function (RBF) regression has recently emerged as a powerful meshless tool for reconstructing continuous velocity fields from scattered flow measurements, particularly in image-based velocimetry. However, existing…

This work describes methodologies to successfully implement the Implicit Monte Carlo (IMC) scheme for thermal radiative transfer in reduced-precision floating-point arithmetic. The methods used can be broadly categorized into scaling…

Nonlinear constrained optimization has a wide range of practical applications. In this paper, we consider nonlinear optimization with inequality constraints. The interior point method is considered to be one of the most powerful algorithms…

The problem of developing an adaptive isogeometric method (AIGM) for solving elliptic second-order partial differential equations with truncated hierarchical B-splines of arbitrary degree and different order of continuity is addressed. The…

Reinforcement fine-tuning (RFT) is a proliferating paradigm for LMM training. Analogous to high-level reasoning tasks, RFT is similarly applicable to low-level vision domains, including image quality assessment (IQA). Existing RFT-based IQA…

Scalable Gaussian Process methods are computationally attractive, yet introduce modeling biases that require rigorous study. This paper analyzes two common techniques: early truncated conjugate gradients (CG) and random Fourier features…