Related papers: Sparse Generalized Eigenvalue Problem via Smooth O…

Several methods have been recently proposed for estimating sparse Gaussian graphical models using $\ell_{1}$ regularization on the inverse covariance matrix. Despite recent advances, contemporary applications require methods that are even…

In this paper, based on a successively accuracy-increasing approximation of the $\ell_0$ norm, we propose a new algorithm for recovery of sparse vectors from underdetermined measurements. The approximations are realized with a certain class…

For the general problem of minimizing a convex function over a compact convex domain, we will investigate a simple iterative approximation algorithm based on the method by Frank & Wolfe 1956, that does not need projection steps in order to…

Sparse (or toric) elimination exploits the structure of polynomials by measuring their complexity in terms of Newton polytopes instead of total degree. The sparse, or Newton, resultant generalizes the classical homogeneous resultant and its…

We study the problem of minimizing the average of a very large number of smooth functions, which is of key importance in training supervised learning models. One of the most celebrated methods in this context is the SAGA algorithm. Despite…

Using gradient descent (GD) with fixed or decaying step-size is a standard practice in unconstrained optimization problems. However, when the loss function is only locally convex, such a step-size schedule artificially slows GD down as it…

This paper introduces an efficient algorithm for finding the dominant generalized eigenvectors of a pair of symmetric matrices. Combining tools from approximation theory and convex optimization, we develop a simple scalable algorithm with…

Tensor completion and robust principal component analysis have been widely used in machine learning while the key problem relies on the minimization of a tensor rank that is very challenging. A common way to tackle this difficulty is to…

In this paper, the generalized eigenvalue complementarity problem for tensors (GEiCP-T) is addressed, which arises from the stability analysis of finite dimensional mechanical systems and find applications in differential dynamical systems.…

Sparsity-constrained optimization is an important and challenging problem that has wide applicability in data mining, machine learning, and statistics. In this paper, we focus on sparsity-constrained optimization in cases where the cost…

We present new convolution based smooth approximations to the absolute value function and apply them to construct gradient based algorithms such as the nonlinear conjugate gradient scheme to obtain sparse, regularized solutions of linear…

The best practical techniques for exact solution of instances of the constrained maximum-entropy sampling problem, a discrete-optimization problem arising in the design of experiments, are via a branch-and-bound framework, working with a…

The Elementary Shortest-Path Problem(ESPP) seeks a minimum cost path from s to t that visits each vertex at most once. The presence of negative-cost cycles renders the problem NP-hard. We present a probabilistic method for finding…

Signomial geometric programming (SGP) is a computationally challenging, NP-Hard class of nonconvex nonlinear optimization problems. SGP can be solved iteratively using a sequence of convex relaxations; consequently, the strength of such…

The sparse optimization problems arise in many areas of science and engineering, such as compressed sensing, image processing, statistical and machine learning. The $\ell_{0}$-minimization problem is one of such optimization problems, which…

We propose and analyze an efficient algorithm for solving the joint sparse recovery problem using a new regularization-based method, named orthogonally weighted $\ell_{2,1}$ ($\mathit{ow}\ell_{2,1}$), which is specifically designed to take…

Efficient exploration is a central problem in reinforcement learning and is often formalized as maximizing the entropy of the state-action occupancy measure. While unconstrained maximum-entropy exploration is relatively well understood,…

We propose an accelerated forward-backward method with fast convergence rate for finding a minimizer of a decomposable nonsmooth convex function over a closed convex set, and name it smoothing accelerated proximal gradient (SAPG) algorithm.…

We describe a novel algorithm for solving general parametric (nonlinear) eigenvalue problems. Our method has two steps: first, high-accuracy solutions of non-parametric versions of the problem are gathered at some values of the parameters;…

Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse…