相关论文: The suppport reduction algorithm for computing non…

Gradient descent algorithms perform well in convex optimization but can get tied for finding local minima in non-convex optimization. A robust method that combines a spectral approach with nonmonotone line search strategy for solving…

We establish the optimal nonergodic sublinear convergence rate of the proximal point algorithm for maximal monotone inclusion problems. First, the optimal bound is formulated by the performance estimation framework, resulting in an infinite…

This paper introduces an abstract framework for randomized subspace correction methods for convex optimization, which unifies and generalizes a broad class of existing algorithms, including domain decomposition, multigrid, and block…

We present an algorithm for minimizing the sum of a strongly convex time-varying function with a time-invariant, convex, and nonsmooth function. The proposed algorithm employs the prediction-correction scheme alongside the forward-backward…

This paper is concerned with solution algorithms for general convex vector optimization problems (CVOPs). So far, solution concepts and approximation algorithms for solving CVOPs exist only for bounded problems [Ararat et al. 2022, Doerfler…

We derive approximation algorithms for the nonnegative matrix factorization problem, i.e. the problem of factorizing a matrix as the product of two matrices with nonnegative coefficients. We form convex approximations of this problem which…

This paper presents a novel learning-based approach to construct a surrogate problem that approximates a given parametric nonconvex optimization problem. The surrogate function is designed to be the minimum of a finite set of functions,…

This paper extends the SQP-approach of the well-known bundle-Newton method for nonsmooth unconstrained minimization to the nonlinearly constrained case. Instead of using a penalty function or a filter or an improvement function to deal with…

We introduce a new approach to develop stochastic optimization algorithms for a class of stochastic composite and possibly nonconvex optimization problems. The main idea is to combine two stochastic estimators to create a new hybrid one. We…

The matrix low-rank approximation problem with additional convex constraints can find many applications and has been extensively studied before. However, this problem is shown to be nonconvex and NP-hard; most of the existing solutions are…

Classical multidimensional scaling only works well when the noisy distances observed in a high dimensional space can be faithfully represented by Euclidean distances in a low dimensional space. Advanced models such as Maximum Variance…

Singular value decomposition (SVD) is one of the most popular compression methods that approximate a target matrix with smaller matrices. However, standard SVD treats the parameters within the matrix with equal importance, which is a simple…

We introduce and analyze an algorithm for the minimization of convex functions that are the sum of differentiable terms and proximable terms composed with linear operators. The method builds upon the recently developed smoothed gap…

We provide the first theoretical analysis on the convergence rate of the asynchronous stochastic variance reduced gradient (SVRG) descent algorithm on non-convex optimization. Recent studies have shown that the asynchronous stochastic…

We propose a new relative-error inexact version of the alternating direction method of multipliers (ADMM) for convex optimization. We prove the asymptotic convergence of our main algorithm as well as pointwise and ergodic…

Reduced order modeling has gained considerable attention in recent decades owing to the advantages offered in reduced computational times and multiple solutions for parametric problems. The focus of this manuscript is the application of…

This paper proposes and develops new Newton-type methods to solve structured nonconvex and nonsmooth optimization problems with justifying their fast local and global convergence by means of advanced tools of variational analysis and…

In the context of convex optimization problems in Hilbert spaces, we induce inertial effects into the classical ADMM numerical scheme and obtain in this way so-called inertial ADMM algorithms, the convergence properties of which we…

Many important machine learning applications involve regularized nonconvex bi-level optimization. However, the existing gradient-based bi-level optimization algorithms cannot handle nonconvex or nonsmooth regularizers, and they suffer from…

We discuss non-Euclidean deterministic and stochastic algorithms for optimization problems with strongly and uniformly convex objectives. We provide accuracy bounds for the performance of these algorithms and design methods which are…