Related papers: The Bregman proximal average
In this paper, we propose a proximal gradient method and an accelerated proximal gradient method for solving composite optimization problems, where the objective function is the sum of a smooth and a convex, possibly nonsmooth, function. We…
We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…
The Laplace approximation is an old, but frequently used method to approximate integrals for Bayesian calculations. In this paper we develop an extension of the Laplace approximation, by applying it iteratively to the residual, i.e., the…
In this paper necessary and sufficient conditions are deduced for the close-to-convexity of some special combinations of Bessel functions of the first kind and their derivatives by using a result of Shah and Trimble about transcendental…
This paper deals with coefficient estimates for close-to-convex functions with argument $\beta$ ($-\pi/2<\beta<\pi/2$). By using Herglotz representation formula, sharp bounds of coefficients are obtained. In particluar, we solve the problem…
This paper derives the exact cumulative density function of the distance between a randomly located node and any arbitrary reference point inside a regular $\el$-sided polygon. Using this result, we obtain the closed-form probability…
We present a tight parametrical Hermite-Hadamard type inequality with probability measure, which yields a considerably closer upper bound for the mean value of convex function than the classical one. Our inequality becomes equality not only…
Persistence diagrams are common objects in the field of Topological Data Analysis. They are topological summaries that capture both topological and geometric structure within data. Recently there has been a surge of interest in developing…
Image analysis frequently deals with shape estimation and image reconstruction. The ob jects of interest in these problems may be thought of as random sets, and one is interested in finding a representative, or expected, set. We consider a…
Problems pointwise estimates from above functions or its averages often arise in the function theory under known integral restrictions on the growth of this function. We offer an approach to such problems based on the integral Jensen's…
We study the variational inference problem of minimizing a regularized R\'enyi divergence over an exponential family. We propose to solve this problem with a Bregman proximal gradient algorithm. We propose a sampling-based algorithm to…
We propose a simple derivation of an upper bound for the perimeter of an ellipse. The procedure, which relies on the use of elliptic integrals, consists in introducing, via inequalities and convexity properties, specific integrals which can…
We prove novel convergence results for a stochastic proximal gradient algorithm suitable for solving a large class of convex optimization problems, where a convex objective function is given by the sum of a smooth and a possibly non-smooth…
This paper introduces a smoothed proximal Lagrangian method for minimizing a nonconvex smooth function over a convex domain with additional explicit convex nonlinear constraints. Two key features are 1) the proposed method is single-looped,…
We revisit the mathematical foundations of proper scoring rules (PSRs) and Bregman divergences and present their characteristic properties in a unified theoretical framework. In many situations it is preferable not to generate a PSR…
We present a generalisation of Rosenblatt's traditional perceptron learning algorithm to the class of proximal activation functions and demonstrate how this generalisation can be interpreted as an incremental gradient method applied to a…
An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…
Recently, Simons provided a lemma for a support function of a closed convex set in a general Hilbert space and used it to prove the geometry conjecture on cycles of projections. In this paper, we extend Simons's lemma to closed convex…
In this paper, we introduce the concept of nearly convex set-valued mappings and investigate fundamental properties of these mappings. Additionally, we establish a geometric approach for generalized differentiation of nearly convex…
We study Bregman proximal augmented Lagrangian methods with second-order oracles for convex convex-composite optimization problems. The outer loop is an instance of the Bregman proximal point algorithm with relative errors in the sense of…