Related papers: Convergence guarantees for stochastic algorithms s…
We investigate an inertial algorithm of gradient type in connection with the minimization of a nonconvex differentiable function. The algorithm is formulated in the spirit of Nesterov's accelerated convex gradient method. We show that the…
An abstract convergence theorem for a class of generalized descent methods that explicitly models relative errors is proved. The convergence theorem generalizes and unifies several recent abstract convergence theorems. It is applicable to…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
Bauschke and Moursi have recently obtained results that implicitly contain the fact that the composition of finitely many averaged mappings on a Hilbert space that have approximate fixed points also has approximate fixed points and thus is…
Many practical optimization problems involve objective function values that are corrupted by unavoidable numerical errors. In smooth nonconvex optimization, quasi-Newton methods combined with line search are widely used due to their…
We present a quasi-Newton method for unconstrained stochastic optimization. Most existing literature on this topic assumes a setting of stochastic optimization in which a finite sum of component functions is a reasonable approximation of an…
We describe inexact proximal Newton-like methods for solving degenerate regularized optimization problems and for the broader problem of finding a zero of a generalized equation that is the sum of a continuous map and a maximal monotone…
Stochastic approximation algorithms are iterative procedures which are used to approximate a target value in an environment where the target is unknown and direct observations are corrupted by noise. These algorithms are useful, for…
This paper presents new sufficient conditions for convergence and asymptotic or exponential stability of a stochastic discrete-time system, under which the constructed Lyapunov function always decreases in expectation along the system's…
We develop a rigorous framework for global non-convex optimization by reformulating the minimization problem as a discounted infinite-horizon optimal control problem. For non-convex, continuous, and possibly non-smooth objective functions…
In this work we deal with the stochastic homogenization of the initial boundary value problems of monotone type. The models of monotone type under consideration describe the deformation behaviour of inelastic materials with a microstructure…
In this paper we show how to accelerate randomized coordinate descent methods and achieve faster convergence rates without paying per-iteration costs in asymptotic running time. In particular, we show how to generalize and efficiently…
We study the asymptotic behavior for an inhomogeneous multiscale stochastic dynamical system with non-smooth coefficients. Depending on the averaging regime and the homogenization regime, two strong convergences in the averaging principle…
Motivated by applications arising from large scale optimization and machine learning, we consider stochastic quasi-Newton (SQN) methods for solving unconstrained convex optimization problems. The convergence analysis of the SQN methods,…
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…
This article is devoted to the analysis of necessary and/or sufficient conditions for metric regularity in terms of Demyanov-Rubinov-Polyakova quasidifferentials. We obtain new necessary and sufficient conditions for the local metric…
Accelerated gradient methods are the cornerstones of large-scale, data-driven optimization problems that arise naturally in machine learning and other fields concerning data analysis. We introduce a gradient-based optimization framework for…
We develop a unified approach to defining a point at infinity for an arbitrary space and formalizing convergence to this point. Central to our work is a method to quantify and classify the rates at which functions approach their limits at…
In 1994, S.G. Matthews introduced the notion of partial metric space in order to obtain a suitable mathematical tool for program verification [Ann. New York Acad. Sci. 728 (1994), 183-197]. He gave an application of this new structure to…
We introduce a new framework for analyzing (Quasi-}Newton type methods applied to non-smooth optimization problems. The source of randomness comes from the evaluation of the (approximation) of the Hessian. We derive, using a variant of…