Related papers: An efficient Hessian based algorithm for solving l…

Gaussian graphical regression is a powerful means that regresses the precision matrix of a Gaussian graphical model on covariates, permitting the numbers of the response variables and covariates to far exceed the sample size. Model fitting…

The paper proposes and develops new globally convergent algorithms of the generalized damped Newton type for solving important classes of nonsmooth optimization problems. These algorithms are based on the theory and calculations of…

This paper studies a class of double-loop (inner-outer) algorithms for convex composite optimization. For unconstrained problems, we develop a restarted accelerated composite gradient method that attains the optimal first-order complexity…

This is an overview paper written in style of research proposal. In recent years we introduced a general framework for large-scale unconstrained optimization -- Sequential Subspace Optimization (SESOP) and demonstrated its usefulness for…

The Lasso is an attractive technique for regularization and variable selection for high-dimensional data, where the number of predictor variables $p_n$ is potentially much larger than the number of samples $n$. However, it was recently…

Graph matching is a challenging problem with very important applications in a wide range of fields, from image and video analysis to biological and biomedical problems. We propose a robust graph matching algorithm inspired in…

We propose an inexact proximal augmented Lagrangian framework with explicit inner problem termination rule for composite convex optimization problems. We consider arbitrary linearly convergent inner solver including in particular stochastic…

We introduce and study the Group Square-Root Lasso (GSRL) method for estimation in high dimensional sparse regression models with group structure. The new estimator minimizes the square root of the residual sum of squares plus a penalty…

We propose a new fast algorithm to estimate any sparse generalized linear model with convex or non-convex separable penalties. Our algorithm is able to solve problems with millions of samples and features in seconds, by relying on…

This paper develops a theory for group Lasso using a concept called strong group sparsity. Our result shows that group Lasso is superior to standard Lasso for strongly group-sparse signals. This provides a convincing theoretical…

We present a sparse Gauss-Newton solver for accelerated sensitivity analysis with applications to a wide range of equilibrium-constrained optimization problems. Dense Gauss-Newton solvers have shown promising convergence rates for inverse…

We present a novel binary convex reformulation of the sparse regression problem that constitutes a new duality perspective. We devise a new cutting plane method and provide evidence that it can solve to provable optimality the sparse…

We study sparse linear regression over a network of agents, modeled as an undirected graph (with no centralized node). The estimation problem is formulated as the minimization of the sum of the local LASSO loss functions plus a quadratic…

Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is done by solving an l_1-regularized linear regression problem, usually called Lasso. In this work we first combine the…

This paper considers a high-dimensional linear regression problem where there are complex correlation structures among predictors. We propose a graph-constrained regularization procedure, named Sparse Laplacian Shrinkage with the Graphical…

Motivated by an inertial primal-dual dynamical system with vanishing damping, we propose a class of accelerated augmented Lagrangian methods with Nesterov extrapolation parameters for a linearly constrained convex optimization problem with…

Solving the distributional worst-case in the distributionally robust optimization problem is equivalent to finding the projection onto the intersection of simplex and singly linear inequality constraint. This projection is a key component…

Square-root (loss) regularized models have recently become popular in linear regression due to their nice statistical properties. Moreover, some of these models can be interpreted as the distributionally robust optimization counterparts of…

The sparse group lasso is a high-dimensional regression technique that is useful for problems whose predictors have a naturally grouped structure and where sparsity is encouraged at both the group and individual predictor level. In this…

In this paper, we propose a distributed Newton method for consensus optimization. Our approach outperforms state-of-the-art methods, including ADMM. The key idea is to exploit the sparsity of the dual Hessian and recast the computation of…