相关论文: Logarithmic convexity of fixed points of stochasti…

The purpose of this paper is to introduce the logarithmic mean of two convex functionals that extends the logarithmic mean of two positive operators. Some inequalities involving this functional mean are discussed as well. The operator…

We study the weak convergence of iterates of so-called centred kernel quadratic stochastic operators. These iterations, in a population evolution setting, describe the additive perturbation of the arithmetic mean of the traits of an…

We present a novel approach to learn a kernel-based regression function. It is based on the useof conical combinations of data-based parameterized kernels and on a new stochastic convex optimization procedure of which we establish…

Most algorithms for solving optimization problems or finding saddle points of convex-concave functions are fixed-point algorithms. In this work we consider the generic problem of finding a fixed point of an average of operators, or an…

We establish some new common fixed point theorems of single-valued and multivalued mappings operating between complete ordered locally convex spaces under weaker assumptions. As an application, we prove a new minimax theorem of existence of…

We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…

A new stochastic primal--dual algorithm for solving a composite optimization problem is proposed. It is assumed that all the functions/operators that enter the optimization problem are given as statistical expectations. These expectations…

We study weak and strong solutions of nonlinear non-compact operator equations in abstract spaces of adapted random points. The main result of the paper is similar to Schauder's fixed-point theorem for compact operators. The illustrative…

In this paper we introduce a notion of $F-$ quadratic stochastic operator. For a wide class of such operators we show that each operator of the class has unique fixed point. Also we prove that any trajectory of the $F$-quadratic stochastic…

We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…

The matrix logarithm, when applied to Hermitian positive definite matrices, is concave with respect to the positive semidefinite order. This operator concavity property leads to numerous concavity and convexity results for other matrix…

Conditions guaranteeing convergence of linear stochastic Volterra operators are studied. Necessary and sufficient conditions for mean square convergence are established, while almost sure convergence of the linear operator is shown to imply…

An usual problem in statistics consists in estimating the minimizer of a convex function. When we have to deal with large samples taking values in high dimensional spaces, stochastic gradient algorithms and their averaged versions are…

Reference [11] investigated the almost sure weak convergence of block-coordinate fixed point algorithms and discussed their applications to nonlinear analysis and optimization. This algorithmic framework features random sweeping rules to…

Any maximal monotone operator can be characterized by a convex function. The family of such convex functions is invariant under a transformation connected with the Fenchel-Legendre conjugation. We prove that there exist a convex…

In this paper, we prove some random fixed point theorems for Hardy-Rogers self-random operators in separable Banach spaces and, as some applications, we show the existence of a solution for random nonlinear integral equations in Banach…

In this paper, we introduce regularized stochastic team problems. Under mild assumptions, we prove that there exists an unique fixed point of the best response operator, where this unique fixed point is the optimal regularized team decision…

This paper deals with homogenization problem for convolution type non-local operators in random statistically homogeneous ergodic media. Assuming that the convolution kernel has a finite second moment and satisfies the uniform ellipticity…

Two optimization algorithms are proposed for solving a stochastic programming problem for which the objective function is given in the form of the expectation of convex functions and the constraint set is defined by the intersection of…

In the article we study properties of the random integral operator in $L_2(\mathbb{R})$ whose kernel is obtained as a convolution of Gaussian density with a stationary point process.