相关论文: Weak Convergence of Approximate reflection couplin…

Strong and weak approximation errors of a spatial finite element method are analyzed for stochastic partial differential equations(SPDEs) with one-sided Lipschitz coefficients, including the stochastic Allen--Cahn equation, driven by…

In this manuscript, we research on the behaviors of surrogates for the rank function on different image processing problems and their optimization algorithms. We first propose a novel nonconvex rank surrogate on the general rank…

We study the convergence of the Augmented Decomposition Algorithm (ADA) proposed in [32] for solving multi-block separable convex minimization problems subject to linear constraints. We show that the global convergence rate of the exact ADA…

This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…

This paper studies a class of convex Finite-sum Coupled Compositional Optimization (cFCCO) problems with applications including group distributionally robust optimization (GDRO) and learning with imbalanced data. To better address these…

Stochastic gradient algorithms estimate the gradient based on only one or a few samples and enjoy low computational cost per iteration. They have been widely used in large-scale optimization problems. However, stochastic gradient algorithms…

A multiconfigurational adiabatic connection (AC) formalism is an attractive approach to computing dynamic correlation within CASSCF and DMRG models. Practical realizations of AC have been based on two approximations: i) fixing one- and…

This paper is devoted to the study of reflected Stochastic Differential Equations when the constraint is not on the paths of the solution but acts on the law of the solution. These reflected equations have been introduced recently by…

Strong convergence rates for numerical approximations of semilinear stochastic partial differential equations (SPDEs) with smooth and regular nonlinearities are well understood in the literature. Weak convergence rates for numerical…

We study the problem of finding a near-stationary point for smooth minimax optimization. The recently proposed extra anchored gradient (EAG) methods achieve the optimal convergence rate for the convex-concave minimax problem in the…

Next-generation wireless communication systems impose much stricter requirements for transmission rate, latency, and reliability. The peak data rate of 6G networks should be no less than 1 Tb/s, which is comparable to existing long-haul…

The scalable adaptive cubic regularization method ($\mathrm{ARC_{q}K}$: Dussault et al. in Math. Program. Ser. A 207(1-2): 191-225, 2024) has been recently proposed for unconstrained optimization. It has excellent convergence properties,…

Difference-of-Convex (DC) minimization, referring to the problem of minimizing the difference of two convex functions, has been found rich applications in statistical learning and studied extensively for decades. However, existing methods…

Given two sets of variables, derived from a common set of samples, sparse Canonical Correlation Analysis (CCA) seeks linear combinations of a small number of variables in each set, such that the induced canonical variables are maximally…

Finite element approximation to a decoupled formulation for the quad--curl problem is studied in this paper. The difficulty of constructing elements with certain conformity to the quad--curl problems has been greatly reduced. For convex…

Under mild conditions on the noise level of the measurements, rotation averaging satisfies strong duality, which enables global solutions to be obtained via semidefinite programming (SDP) relaxation. However, generic solvers for SDP are…

We propose a novel approach to approximate Bayesian computation (ABC) that seeks to cater for possible misspecification of the assumed model. This new approach can be equally applied to rejection-based ABC and to popular regression…

Communication remains a central bottleneck in large-scale distributed machine learning, and gradient sparsification has emerged as a promising strategy to alleviate this challenge. However, existing gradient compressors face notable…

Motivated by learning of correlated equilibria in non-cooperative games, we perform a large deviations analysis of a regret minimizing stochastic approximation algorithm. The regret minimization algorithm we consider comprises multiple…

The state-of-the-art methods for solving optimization problems in big dimensions are variants of randomized coordinate descent (RCD). In this paper we introduce a fundamentally new type of acceleration strategy for RCD based on the…