相关论文: On Quadratic Convergence of DC Proximal Newton Alg…

We introduce a novel algorithm for solving learning problems where both the loss function and the regularizer are non-convex but belong to the class of difference of convex (DC) functions. Our contribution is a new general purpose proximal…

The paper proposes and justifies a new algorithm of the proximal Newton type to solve a broad class of nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions and techniques of…

We consider a class of difference-of-convex (DC) optimization problems where the objective function is the sum of a smooth function and a possible nonsmooth DC function. The application of proximal DC algorithms to address this problem…

In this paper, we propose new methods to efficiently solve convex optimization problems encountered in sparse estimation, which include a new quasi-Newton method that avoids computing the Hessian matrix and improves efficiency, and we prove…

Nonconvex sparse models have received significant attention in high-dimensional machine learning. In this paper, we study a new model consisting of a general convex or nonconvex objectives and a variety of continuous nonconvex…

We address the minimization of a smooth objective function under an $\ell_0$-constraint and simple convex constraints. When the problem has no constraints except the $\ell_0$-constraint, some efficient algorithms are available; for example,…

This paper focuses on stochastic proximal gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer and convex constraints. To the best of our knowledge we present the first non-asymptotic…

Sparse learning is a very important tool for mining useful information and patterns from high dimensional data. Non-convex non-smooth regularized learning problems play essential roles in sparse learning, and have drawn extensive attentions…

Motivated by the need for decentralized learning, this paper aims at designing a distributed algorithm for solving nonconvex problems with general linear constraints over a multi-agent network. In the considered problem, each agent owns…

Correspondence problems are often modelled as quadratic optimization problems over permutations. Common scalable methods for approximating solutions of these NP-hard problems are the spectral relaxation for non-convex energies and the…

We consider concave minimization problems over non-convex sets.Optimization problems with this structure arise in sparse principal component analysis. We analyze both a gradient projection algorithm and an approximate Newton algorithm where…

Sparse inverse covariance selection is a fundamental problem for analyzing dependencies in high dimensional data. However, such a problem is difficult to solve since it is NP-hard. Existing solutions are primarily based on convex…

We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints. Sufficient conditions are provided, under which the proposed algorithm enjoys strong linear convergence…

Sparse optimization refers to an optimization problem involving the zero-norm in objective or constraints. In this paper, nonconvex approximation approaches for sparse optimization have been studied with a unifying point of view in DC…

In this paper, we propose new proximal Newton-type methods for convex optimization problems in composite form. The applications include model predictive control (MPC) and embedded MPC. Our new methods are computationally attractive since…

We propose an algorithmic framework for convex minimization problems of a composite function with two terms: a self-concordant function and a possibly nonsmooth regularization term. Our method is a new proximal Newton algorithm that…

In this paper, we develop a randomized algorithm and theory for learning a sparse model from large-scale and high-dimensional data, which is usually formulated as an empirical risk minimization problem with a sparsity-inducing regularizer.…

We propose a randomized algorithm with quadratic convergence rate for convex optimization problems with a self-concordant, composite, strongly convex objective function. Our method is based on performing an approximate Newton step using a…

In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form…

In this paper, a multi-parameterized proximal point algorithm combining with a relaxation step is developed for solving convex minimization problem subject to linear constraints. We show its global convergence and sublinear convergence rate…