Related papers: Methods for Solving Variational Inequalities with …
We consider stochastic optimization problems involving an expected value of a nonlinear function of a base random vector and a conditional expectation of another function depending on the base random vector, a dependent random vector, and…
In this paper, we address a manifold constrained nonsmooth optimization problem involving the composition of a weakly convex function and a smooth mapping under the availability of a parametrization of the manifold. To find a stationary…
We study a class of second order variational inequalities with bilateral constraints. Under certain conditions we show the existence of a unique viscosity solution of these variational inequalities and give a stochastic representation to…
We propose an algorithm for optimizations in which the gradients contain stochastic noise. This arises, for example, in structural optimizations when computations of forces and stresses rely on methods involving Monte Carlo sampling, such…
In this paper, we propose a unified view of gradient-based algorithms for stochastic convex composite optimization by extending the concept of estimate sequence introduced by Nesterov. More precisely, we interpret a large class of…
Stochastic Approximation has been a prominent set of tools for solving problems with noise and uncertainty. Increasingly, it becomes important to solve optimization problems wherein there is noise in both a set of constraints that a…
We present an optimization-based method for the joint estimation of system parameters and noise covariances of linear time-variant systems. Given measured data, this method maximizes the likelihood of the parameters. We solve the…
In this note we investigate stochastic Nash equilibrium problems by means of monotone variational inequalities in probabilistic Lebesgue spaces. We apply our approach to a class of oligopolistic market equilibrium problems where the data…
This paper is a survey of methods for solving smooth (strongly) monotone stochastic variational inequalities. To begin with, we give the deterministic foundation from which the stochastic methods eventually evolved. Then we review methods…
In this paper, we study the local linear convergence behavior of proximal-gradient (PG) descent algorithm on a parameterized gap-function reformulation of a smooth but non-monotone variational inequality problem (VIP). The aim is to solve…
Approximating complex probability densities is a core problem in modern statistics. In this paper, we introduce the concept of Variational Inference (VI), a popular method in machine learning that uses optimization techniques to estimate…
We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints. Sufficient conditions are provided, under which the proposed algorithm enjoys strong linear convergence…
In this paper, we propose a new policy iteration algorithm to compute the value function and the optimal controls of continuous time stochastic control problems. The algorithm relies on successive approximations using linear-quadratic…
Motivated by multi-user optimization problems and non-cooperative Nash games in stochastic regimes, we consider stochastic variational inequality (SVI) problems on matrix spaces where the variables are positive semidefinite matrices and the…
The objective of this research is to explore a convex feasibility problem, which consists of a monotone variational inequality problem and a fixed point problem. We introduce four inertial extragradient algorithms that are motivated by the…
We develop a novel optimistic gradient-type algorithmic framework, combining both Nesterov's acceleration and variance-reduction techniques, to solve a class of generalized equations involving possibly nonmonotone operators in data-driven…
Semilinear stochastic evolution equations with multiplicative L\'evy noise and monotone nonlinear drift are considered. Unlike other similar work we do not impose coercivity conditions on coefficients. Existence and uniqueness of the mild…
In this paper, we propose a new way to obtain optimal convergence rates for smooth stochastic (strong) convex optimization tasks. Our approach is based on results for optimization tasks where gradients have nonrandom noise. In contrast to…
We consider the problem of approximation of the solution of the backward stochastic differential equation in the Markovian case. We suppose that the trend coefficient of the diffusion process depends on some unknown parameter and the…
Motivated by broad applications in machine learning, we study the popular accelerated stochastic gradient descent (ASGD) algorithm for solving (possibly nonconvex) optimization problems. We characterize the finite-time performance of this…