Related papers: The Localization Method for High-Dimensional Inequ…
In this paper we present a convergence rate analysis of inexact variants of several randomized iterative methods. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic…
We derive exact quantum expressions for the localization length $L_c$ for weak disorder in two- and three chain tight-binding systems coupled by random nearest-neighbour interchain hopping terms and including random energies of the atomic…
We propose a multiscale approach for an elliptic multiscale setting with general unstructured diffusion coefficients that is able to achieve high-order convergence rates with respect to the mesh parameter and the polynomial degree. The…
The multistage stochastic variational inequality is reformulated into a variational inequality with separable structure through introducing a new variable. The prediction-correction ADMM which was originally proposed in [B.-S. He, L.-Z.…
We propose a simple, yet powerful regularization technique that can be used to significantly improve both the pairwise and triplet losses in learning local feature descriptors. The idea is that in order to fully utilize the expressive power…
We introduce new multilevel methods for solving large-scale unconstrained optimization problems. Specifically, the philosophy of multilevel methods is applied to Newton-type methods that regularize the Newton sub-problem using second order…
A new adaptive approach is proposed for variational inequalities with a Lipschitz-continuous field. Estimates of the necessary number of iterations are obtained to achieve a given quality of the variational inequality solution. A…
The problem of minimizing a separable convex function under linearly coupled constraints arises from various application domains such as economic systems, distributed control, and network flow. The main challenge for solving this problem is…
The likelihood-informed subspace (LIS) method offers a viable route to reducing the dimensionality of high-dimensional probability distributions arising in Bayesian inference. LIS identifies an intrinsic low-dimensional linear subspace…
Decentralized optimization for non-convex problems are now demanding by many emerging applications (e.g., smart grids, smart building, etc.). Though dramatic progress has been achieved in convex problems, the results for non-convex cases,…
This paper considers covariance matrix estimation of tensor data under high dimensionality. A multi-bandable covariance class is established to accommodate the need for complex covariance structures of multi-layer lattices and general…
Majorization-minimization schemes are a broad class of iterative methods targeting general optimization problems, including nonconvex, nonsmooth and stochastic. These algorithms minimize successively a sequence of upper bounds of the…
Visual localization under large changes in scale is an important capability in many robotic mapping applications, such as localizing at low altitudes in maps built at high altitudes, or performing loop closure over long distances. Existing…
In this paper, a synthesis method for distributed estimation is presented, which is suitable for dealing with large-scale interconnected linear systems with disturbance. The main feature of the proposed method is that local estimators only…
In this two-part study we develop a unified approach to the analysis of the global exactness of various penalty and augmented Lagrangian functions for finite-dimensional constrained optimization problems. This approach allows one to verify…
Stochastic methods for minimizing a convex integral functional, as initiated by Robbins and Monro in the early 1950s, rely on the evaluation of a gradient (or subgradient if the function is not smooth) and moving in the corresponding…
The Carleman embedding method is a widely used technique for linearizing a system of nonlinear differential equations, but fails to converge in regions where there are multiple fixed points. We propose and test three different versions of a…
This paper discusses a methodology for determining a functional representation of a random process from a collection of scattered pointwise samples. The present work specifically focuses onto random quantities lying in a high dimensional…
We develop a new method to obtain symmetrization inequalities of Sobolev type. Our approach leads to new inequalities and considerable simplification in the theory of embeddings of Sobolev spaces based on rearrangement invariant spaces.
Distributed optimization has many applications, in communication networks, sensor networks, signal processing, machine learning, and artificial intelligence. Methods for distributed convex optimization are widely investigated, while those…