相关论文: A proximal dual semismooth Newton method for compu…

Adaptive nuclear-norm penalization is proposed for low-rank matrix approximation, by which we develop a new reduced-rank estimation method for the general high-dimensional multivariate regression problems. The adaptive nuclear norm of a…

We propose a novel multi-layer neural network architecture that gives a promising neural network empowered optimization approach to the image restoration problem. The proposed architecture is motivated by the recent study of monotone…

Finding an $\epsilon$-stationary point of a nonconvex function with a Lipschitz continuous Hessian is a central problem in optimization. Regularized Newton methods are a classical tool and have been studied extensively, yet they still face…

Multicriterion optimization and Pareto optimality are fundamental tools in economics. In this paper we propose a new relaxation method for solving multiple objective quadratic programming problems. Exploiting the technique of the linear…

This technical note studies a class of distributed nonsmooth convex consensus optimization problem. The cost function is a summation of local cost functions which are convex but nonsmooth. Each of the local cost functions consists of a…

We propose an inexact variable-metric proximal point algorithm to accelerate gradient-based optimization algorithms. The proposed scheme, called QNing can be notably applied to incremental first-order methods such as the stochastic…

In this paper, we develop a parameterized proximal point algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent…

Several decades ago the Proximal Point Algorithm (PPA) started to gain a long-lasting attraction for both abstract operator theory and numerical optimization communities. Even in modern applications, researchers still use proximal…

Finding a zero of a maximal monotone operator is fundamental in convex optimization and monotone operator theory, and \emph{proximal point algorithm} (PPA) is a primary method for solving this problem. PPA converges not only globally under…

We introduce the primal-dual quasi-Newton (PD-QN) method as an approximated second order method for solving decentralized optimization problems. The PD-QN method performs quasi-Newton updates on both the primal and dual variables of the…

Recent theoretical studies proved that deep neural network (DNN) estimators obtained by minimizing empirical risk with a certain sparsity constraint can attain optimal convergence rates for regression and classification problems. However,…

Support Vector Machines (SVMs) are among the most popular and the best performing classification algorithms. Various approaches have been proposed to reduce the high computation and memory cost when training and predicting based on…

Rank minimization (RM) is a wildly investigated task of finding solutions by exploiting low-rank structure of parameter matrices. Recently, solving RM problem by leveraging non-convex relaxations has received significant attention. It has…

In this paper, we propose a new algorithm for recovery of low-rank matrices from compressed linear measurements. The underlying idea of this algorithm is to closely approximate the rank function with a smooth function of singular values,…

Many results have been proved for various nuclear norm penalized estimators of the uniform sampling matrix completion problem. However, most of these estimators are not robust: in most of the cases the quadratic loss function and its…

For the problem of reconstructing a low-rank matrix from a few linear measurements, two classes of algorithms have been widely studied in the literature: convex approaches based on nuclear norm minimization, and non-convex approaches that…

We propose a novel stochastic approximation algorithm, termed PMQSopt, for solving weakly convex stochastic optimization problems involving expectation-valued functions. The algorithm is constructed by integrating the proximal method of…

We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving ERM problems with a nonsmooth regularization term. Current second-order and quasi-Newton methods for this…

For regularized optimization that minimizes the sum of a smooth term and a regularizer that promotes structured solutions, inexact proximal-Newton-type methods, or successive quadratic approximation (SQA) methods, are widely used for their…

The continuous quadratic knapsack (CQK) problem involves minimizing a diagonal convex quadratic function subject to box constraints and a single linear equality constraint. It has numerous applications in resource allocation, multicommodity…