Related papers: A Fully Sparse Implementation of a Primal-Dual Int…
Interpolation-based trust-region methods are an important class of algorithms for Derivative-Free Optimization which rely on locally approximating an objective function by quadratic polynomial interpolation models, frequently built from…
We explore algorithms and limitations for sparse optimization problems such as sparse linear regression and robust linear regression. The goal of the sparse linear regression problem is to identify a small number of key features, while the…
In this paper we develop a novel approach for estimating large and sparse dynamic factor models using variational inference, also allowing for missing data. Inspired by Bayesian variable selection, we apply slab-and-spike priors onto the…
We consider the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse. Our approach is to solve a maximum likelihood problem with an added l_1-norm…
In semidefinite programming (SDP), a number of pre-processing techniques have been developed including chordal-completion procedures, which reduce the dimension of individual constraints by exploiting sparsity therein, and facial reduction,…
Sparsity-constrained optimization has wide applicability in machine learning, statistics, and signal processing problems such as feature selection and compressive Sensing. A vast body of work has studied the sparsity-constrained…
This paper proposes a new method for estimating sparse precision matrices in the high dimensional setting. It has been popular to study fast computation and adaptive procedures for this problem. We propose a novel approach, called Sparse…
Thirty years ago, in a seminal paper Ramana derived an exact dual for Semidefinite Programming (SDP). Ramana's dual has the following remarkable features: i) it is an explicit, polynomial size semidefinite program ii) it does not assume…
In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature…
This paper proposes an Adaptive Stochastic Model Predictive Control (MPC) strategy for stable linear time-invariant systems in the presence of bounded disturbances. We consider multi-input, multi-output systems that can be expressed by a…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
Dynamic sparsity, where the sparsity patterns are unknown until runtime, poses a significant challenge to deep learning. The state-of-the-art sparsity-aware deep learning solutions are restricted to pre-defined, static sparsity patterns due…
Our work considers the optimization of the sum of a non-smooth convex function and a finite family of composite convex functions, each one of which is composed of a convex function and a bounded linear operator. This type of problem is…
Sparse support recovery arises in many applications in communications and signal processing. Existing methods tackle sparse support recovery problems for a given measurement matrix, and cannot flexibly exploit the properties of sparsity…
In dictionary learning, also known as sparse coding, the algorithm is given samples of the form $y = Ax$ where $x\in \mathbb{R}^m$ is an unknown random sparse vector and $A$ is an unknown dictionary matrix in $\mathbb{R}^{n\times m}$…
We study the problem of hyperparameter tuning in sparse matrix factorization under Bayesian framework. In the prior work, an analytical solution of sparse matrix factorization with Laplace prior was obtained by variational Bayes method…
Sparse modelling or model selection with categorical data is challenging even for a moderate number of variables, because one parameter is roughly needed to encode one category or level. The Group Lasso is a well known efficient algorithm…
Given a sample covariance matrix, we solve a maximum likelihood problem penalized by the number of nonzero coefficients in the inverse covariance matrix. Our objective is to find a sparse representation of the sample data and to highlight…
In recent years, many estimation problems in robotics have been shown to be solvable to global optimality using their semidefinite relaxations. However, the runtime complexity of off-the-shelf semidefinite programming (SDP) solvers is up to…
Semi-Infinite Programming (SIP) has emerged as a powerful framework for modeling problems with infinite constraints, however, its theoretical development in the context of nonconvex and large-scale optimization remains limited. In this…