Related papers: Mixed Finite Differences Scheme for Gradient Appro…
In min-min optimization or max-min optimization, one has to compute the gradient of a function defined as a minimum. In most cases, the minimum has no closed-form, and an approximation is obtained via an iterative algorithm. There are two…
The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques…
Motivated by applications to stochastic programming, we introduce and study the expected-integral functionals, which are mappings given in an integral form depending on two variables, the first a finite dimensional decision vector and the…
The article considers the discrete analogue of the method of quickest descent for an inverse Acoustics problem in case of a smooth source. The authors derived the gradient of functional in differential and discrete cases, described the…
We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…
In this work, we consider the problem of distributed approximation of functions over multiple-access channels with additive noise. In contrast to previous works, we take fast fading into account and give explicit probability bounds for the…
Gradient matching with Gaussian processes is a promising tool for learning parameters of ordinary differential equations (ODE's). The essence of gradient matching is to model the prior over state variables as a Gaussian process which…
Standard approaches to stochastic gradient estimation, with only noisy black-box function evaluations, use the finite-difference method or its variants. While natural, it is open to our knowledge whether their statistical accuracy is the…
This paper aims at achieving a "good" estimator for the gradient of a function on a high-dimensional space. Often such functions are not sensitive in all coordinates and the gradient of the function is almost sparse. We propose a method for…
Gradient approximations are a class of numerical approximation techniques that are of central importance in numerical optimization. In derivative-free optimization, most of the gradient approximations, including the simplex gradient,…
This paper is concerned with goal-oriented a posteriori error estimation for nonlinear functionals in the context of nonlinear variational problems solved with continuous Galerkin finite element discretizations. A two-level, or discrete,…
It is well-known that non-linear approximation has an advantage over linear schemes in the sense that it provides comparable approximation rates to those of the linear schemes, but to a larger class of approximands. This was established for…
A new notion of metric differentiability of set-valued functions at a point is introduced in terms of right and left limits of special set-valued metric divided differences of first order. A local metric linear approximant of a metrically…
This work proposes a machine-learning framework for constructing statistical models of errors incurred by approximate solutions to parameterized systems of nonlinear equations. These approximate solutions may arise from early termination of…
The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item $i$ is closer to item $j$ than item $k$". Ordinal constraints like…
We investigate smooth approximations of functions, with prescribed gradient behavior on a distinguished stratified subset of the domain. As an application, we outline how our results yield important consequences for a recently introduced…
Gradient methods are experiencing a growth in methodological and theoretical developments owing to the challenges posed by optimization problems arising in data science. However, such gradient methods face diverging optimality gaps or…
In this paper, we present a stochastic gradient algorithm for minimizing a smooth objective function that is an expectation over noisy cost samples, and only the latter are observed for any given parameter. Our algorithm employs a gradient…
Many problems involve the use of models which learn probability distributions or incorporate randomness in some way. In such problems, because computing the true expected gradient may be intractable, a gradient estimator is used to update…
In this paper we consider finite sum composite convex optimization problems with many functional constraints. The objective function is expressed as a finite sum of two terms, one of which admits easy computation of (sub)gradients while the…