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In this paper, we study the problem of distributed multi-agent optimization over a network, where each agent possesses a local cost function that is smooth and strongly convex. The global objective is to find a common solution that…
We study the conjugate gradient method for solving s system of linear equations with coefficients which are measurable functions and establish the rate of convergence of this method.
A generalized conditional gradient method for minimizing the sum of two convex functions, one of them differentiable, is presented. This iterative method relies on two main ingredients: First, the minimization of a partially linearized…
Modern large-scale statistical models require to estimate thousands to millions of parameters. This is often accomplished by iterative algorithms such as gradient descent, projected gradient descent or their accelerated versions. What are…
Identification of cracks is essential to assess the structural integrity of concrete infrastructure. However, robust crack segmentation remains a challenging task for computer vision systems due to the diverse appearance of concrete…
We consider the problem of numerical approximation of integrals of random fields over a unit hypercube. We use a stratified Monte Carlo quadrature and measure the approximation performance by the mean squared error. The quadrature is…
Irregular boundary lines can be characterized by fractal dimension, which provides important information for spatial analysis of complex geographical phenomena such as cities. However, it is difficult to calculate fractal dimension of…
The aim of this paper is to present the convergence analysis of a very general class of gradient projection methods for smooth, constrained, possibly nonconvex, optimization. The key features of these methods are the Armijo linesearch along…
Gradient estimation -- approximating the gradient of an expectation with respect to the parameters of a distribution -- is central to the solution of many machine learning problems. However, when the distribution is discrete, most common…
We propose a general procedure for estimating the variance-covariance matrix of two-step estimates of structural parameters in latent variable models. The method is partially simulation-based, in that it includes drawing simulated values of…
Normal estimation for 3D point clouds is a fundamental task in 3D geometry processing. The state-of-the-art methods rely on priors of fitting local surfaces learned from normal supervision. However, normal supervision in benchmarks comes…
Seismic tomography is a methodology to image the interior of solid or fluid media, and is often used to map properties in the subsurface of the Earth. In order to better interpret the resulting images it is important to assess imaging…
This paper proposes a Direct Rational Radial Basis Functions Partition of Unity (D-RRBF-PU) approach to compute derivatives of functions with steep gradients or discontinuities. The novelty of the method concerns how derivatives are…
We introduce a family of pairwise stochastic gradient estimators for gradients of expectations, which are related to the log-derivative trick, but involve pairwise interactions between samples. The simplest example of our new estimator,…
We propose to differentiate a general curvature functional with two different approaches. In the first one we compute the derivative with the tools of shape optimization and in the second one we compute the derivative of a volumic…
The adjoint method is an efficient way to numerically compute gradients in optimization problems with constraints, but is only formulated to differentiable cost and constraint functions on real variables. With the introduction of complex…
Global variational approximation methods in graphical models allow efficient approximate inference of complex posterior distributions by using a simpler model. The choice of the approximating model determines a tradeoff between the…
Splitting methods constitute a widely used class of numerical integrators for ordinary and partial differential equations, particularly well suited to problems that can be decomposed into simpler subproblems. High-order splitting schemes…
Gradient matching is a promising tool for learning parameters and state dynamics of ordinary differential equations. It is a grid free inference approach, which, for fully observable systems is at times competitive with numerical…
This paper reviews the gradient sampling methodology for solving nonsmooth, nonconvex optimization problems. An intuitively straightforward gradient sampling algorithm is stated and its convergence properties are summarized. Throughout this…