Related papers: Dual Newton Proximal Point Algorithm for Solution …
This paper proposes new proximal Newton-type methods with a diagonal metric for solving composite optimization problems whose objective function is the sum of a twice continuously differentiable function and a proper closed directionally…
In this paper, we investigate a second-order stochastic algorithm for solving large-scale binary classification problems. We propose to make use of a new hybrid stochastic Newton algorithm that includes two weighted components in the…
Many machine learning models involve solving optimization problems. Thus, it is important to deal with a large-scale optimization problem in big data applications. Recently, subsampled Newton methods have emerged to attract much attention…
In this paper, we introduce a proximal-proximal majorization-minimization (PPMM) algorithm for nonconvex tuning-free robust regression problems. The basic idea is to apply the proximal majorization-minimization algorithm to solve the…
Motivated by economic dispatch and linearly-constrained resource allocation problems, this paper proposes a class of novel Distributed-Approx Newton algorithms that approximate the standard Newton optimization method. We first develop the…
The goal of this paper is to study approaches to bridge the gap between first-order and second-order type methods for composite convex programs. Our key observations are: i) Many well-known operator splitting methods, such as…
In this paper we propose a primal-dual proximal extragradient algorithm to solve the generalized Dantzig selector (GDS) estimation problem, based on a new convex-concave saddle-point (SP) reformulation. Our new formulation makes it possible…
This paper studies how to train machine-learning models that directly approximate the optimal solutions of constrained optimization problems. This is an empirical risk minimization under constraints, which is challenging as training must…
The $L_1$-regularized models are widely used for sparse regression or classification tasks. In this paper, we propose the orthant-wise passive descent algorithm (OPDA) for optimizing $L_1$-regularized models, as an improved substitute of…
Logistic regression is a well-known statistical model which is commonly used in the situation where the output is a binary random variable. It has a wide range of applications including machine learning, public health, social sciences,…
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…
This paper aims to devise an adaptive neural network basis method for numerically solving a second-order semilinear partial differential equation (PDE) with low-regular solutions in two/three dimensions. The method is obtained by combining…
Second-order methods are of great importance for composite convex optimization problems due to their local super-linear convergence rates (under appropriate assumptions). However, the presence of even a simple nonsmooth function in the…
We introduce a new second order stochastic algorithm to estimate the entropically regularized optimal transport cost between two probability measures. The source measure can be arbitrary chosen, either absolutely continuous or discrete,…
We investigate the proximal point algorithm (PPA) and its inexact extensions under an error bound condition, which guarantees a global linear convergence if the proximal regularization parameter is larger than the error bound condition…
Newton's method is the most widespread high-order method, demanding the gradient and the Hessian of the objective function. However, one of the main disadvantages of Newtons method is its lack of global convergence and high iteration cost.…
The high-dimensional rank lasso (hdr lasso) model is an efficient approach to deal with high-dimensional data analysis. It was proposed as a tuning-free robust approach for the high-dimensional regression and was demonstrated to enjoy…
In this paper, we are motivated by two important applications: entropy-regularized optimal transport problem and road or IP traffic demand matrix estimation by entropy model. Both of them include solving a special type of optimization…
There is a recent interest on first-order methods for linear programming (LP). In this paper,we propose a stochastic algorithm using variance reduction and restarts for solving sharp primal-dual problems such as LP. We show that the…
This paper aims to address distributed optimization problems over directed and time-varying networks, where the global objective function consists of a sum of locally accessible convex objective functions subject to a feasible set…