Related papers: Nonstationary iterative processes
We describe convergence acceleration schemes for multistep optimization algorithms. The extrapolated solution is written as a nonlinear average of the iterates produced by the original optimization method. Our analysis does not need the…
Iterative algorithms are fundamental tools for approximating fixed-points of nonexpansive operators in real Hilbert spaces. Among them, Krasnosel'ski\u{\i}--Mann iteration and Halpern iteration are two widely used schemes. In this work, we…
This paper introduces progressive algorithms for the topological analysis of scalar data. Our approach is based on a hierarchical representation of the input data and the fast identification of topologically invariant vertices, which are…
Bayesian optimization has shown to be a fundamental global optimization algorithm in many applications: ranging from automatic machine learning, robotics, reinforcement learning, experimental design, simulations, etc. The most popular and…
This paper presents a probabilistic perspective on iterative methods for approximating the solution $\mathbf{x}_* \in \mathbb{R}^d$ of a nonsingular linear system $\mathbf{A} \mathbf{x}_* = \mathbf{b}$. In the approach a standard iterative…
We consider infinite-horizon $\gamma$-discounted Markov Decision Processes, for which it is known that there exists a stationary optimal policy. We consider the algorithm Value Iteration and the sequence of policies $\pi_1,...,\pi_k$ it…
We propose a novel approach for change-point detection and parameter learning in multivariate non-stationary time series exhibiting oscillatory behaviour. We approximate the process through a piecewise function defined by a sum of…
Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little…
Co-simulation is widely used in the industry due to the emergence of modular dynamical models made up of interconnected, black-boxed systems. Several co-simulation algorithms have been developed, each with different properties and different…
As first-order optimization methods become the method of choice for solving large-scale optimization problems, optimization solvers based on first-order algorithms are being built. Such general-purpose solvers must robustly detect…
Distributed network optimization has been studied for well over a decade. However, we still do not have a good idea of how to design schemes that can simultaneously provide good performance across the dimensions of utility optimality,…
The paper is devoted to the development of a methodology for evaluating the scalability of compute-intensive iterative algorithms used in simulating complex physical processes on supercomputer systems. The proposed methodology is based on…
Visibility algorithms are a family of methods to map time series into networks, with the aim of describing the structure of time series and their underlying dynamical properties in graph-theoretical terms. Here we explore some properties of…
This paper is concerned with the study of a family of fixed point iterations combining relaxation with different inertial (acceleration) principles. We provide a systematic, unified and insightful analysis of the hypotheses that ensure…
By using the Ishikawa iterative algorithm, we approximate the fixed points and the best proximity points of a relatively non expansive mapping. Also, we use the von Neumann sequence to prove the convergence result in a Hilbert space…
Computer experiments can emulate the physical systems, help computational investigations, and yield analytic solutions. They have been widely employed with many engineering applications (e.g., aerospace, automotive, energy systems.…
The iterative problem of solving nonlinear equations is studied. A new Newton like iterative method with adjustable parameters is designed based on the dynamic system theory. In order to avoid the derivative function in the iterative…
We propose new continuous-time formulations for first-order stochastic optimization algorithms such as mini-batch gradient descent and variance-reduced methods. We exploit these continuous-time models, together with simple Lyapunov analysis…
This paper proposes a general incremental policy iteration adaptive dynamic programming (ADP) algorithm for model-free robust optimal control of unknown nonlinear systems. The approach integrates recursive least squares estimation with…
In this paper we propose an approach for solving systems of nonlinear equations without computing function derivatives. Motivated by the application area of tomographic absorption spectroscopy, which is a highly-nonlinear problem with…