相关论文: A proximal Newton framework for composite minimiza…

We extend the standard notion of self-concordance to non-convex optimization and develop a family of second-order algorithms with global convergence guarantees. In particular, two function classes -- \textit{weakly self-concordant}…

Graph learning problems are typically approached by focusing on learning the topology of a single graph when signals from all nodes are available. However, many contemporary setups involve multiple related networks and, moreover, it is…

We study the problem of prediction for evolving graph data. We formulate the problem as the minimization of a convex objective encouraging sparsity and low-rank of the solution, that reflect natural graph properties. The convex formulation…

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…

A number of inference problems with sensor networks involve projecting a measured signal onto a given subspace. In existing decentralized approaches, sensors communicate with their local neighbors to obtain a sequence of iterates that…

Optimization algorithms for solving nonconvex inverse problem have attracted significant interests recently. However, existing methods require the nonconvex regularization to be smooth or simple to ensure convergence. In this paper, we…

We propose a unified derivative-free proximal Newton-type algorithm framework for solving composite optimization problems formulated as the sum of a black-box function and a known regularization term. We establish the iteration and oracle…

This work introduces a simple and efficient linesearch method for composite minimization that accelerates proximal-gradient iterations with fast Newton-type directions. Our algorithm is based on simple operations and only requires the…

In [19], a general, inexact, efficient proximal quasi-Newton algorithm for composite optimization problems has been proposed and a sublinear global convergence rate has been established. In this paper, we analyze the convergence properties…

A novel Gromov-Wasserstein learning framework is proposed to jointly match (align) graphs and learn embedding vectors for the associated graph nodes. Using Gromov-Wasserstein discrepancy, we measure the dissimilarity between two graphs and…

We consider the class of convex minimization problems, composed of a self-concordant function, such as the $\log\det$ metric, a convex data fidelity term $h(\cdot)$ and, a regularizing -- possibly non-smooth -- function $g(\cdot)$. This…

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…

We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…

In this paper, a globally convergent Newton-type proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…

Within the unmanageably large class of nonconvex optimization, we consider the rich subclass of nonsmooth problems that have composite objectives---this already includes the extensively studied convex, composite objective problems as a…

We propose a novel trust region method for solving a class of nonsmooth, nonconvex composite-type optimization problems. The approach embeds inexact semismooth Newton steps for finding zeros of a normal map-based stationarity measure for…

We propose a conditional gradient framework for a composite convex minimization template with broad applications. Our approach combines smoothing and homotopy techniques under the CGM framework, and provably achieves the optimal…

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…

Learning a graph topology to reveal the underlying relationship between data entities plays an important role in various machine learning and data analysis tasks. Under the assumption that structured data vary smoothly over a graph, the…

Sparse high dimensional graphical model selection is a popular topic in contemporary machine learning. To this end, various useful approaches have been proposed in the context of $\ell_1$-penalized estimation in the Gaussian framework.…