Related papers: The Sparse Solution to $\mathcal{KS}$-Tensor Compl…
We present and analyze a simple, two-step algorithm to approximate the optimal solution of the sparse PCA problem. Our approach first solves a L1 penalized version of the NP-hard sparse PCA optimization problem and then uses a randomized…
The composite $L_q~(0<q<1)$ minimization problem over a general polyhedron has received various applications in machine learning, wireless communications, image restoration, signal reconstruction, etc. This paper aims to provide a…
Representing signals with sparse vectors has a wide range of applications that range from image and video coding to shape representation and health monitoring. In many applications with real-time requirements, or that deal with…
As enjoying the closed form solution, least squares support vector machine (LSSVM) has been widely used for classification and regression problems having the comparable performance with other types of SVMs. However, LSSVM has two drawbacks:…
Sparse tensor algebra is challenging to efficiently parallelize due to the irregular, data-dependent, and potentially skewed structure of sparse computation. We propose the first partitioning algorithm that provably load balances the…
In this work, we propose an algorithm for solving exact sparse linear regression problems over a network in a distributed manner. Particularly, we consider the problem where data is stored among different computers or agents that seek to…
We study the ternary quadratic problem (TQP), a quadratic optimization problem with linear constraints where the variables take values in $\{0, \pm 1\}$. While semidefinite programming (SDP) techniques are well established for $\{0,1\}$-…
Sparsity is a fundamental modeling principle in statistics, signal processing, and data science. However, optimization with sparsity constraints is notoriously difficult. We introduce a new convex relaxation framework for {sparse…
The standard quadratic optimization problem (StQP), i.e. the problem of minimizing a quadratic form $\bold x^TQ\bold x$ on the standard simplex $\{\bold x\ge\bold 0: \bold x^T\bold e=1\}$, is studied. The StQP arises in numerous…
We formulate the sparse classification problem of $n$ samples with $p$ features as a binary convex optimization problem and propose a cutting-plane algorithm to solve it exactly. For sparse logistic regression and sparse SVM, our algorithm…
We give an efficient algorithm for finding sparse approximate solutions to linear systems of equations with nonnegative coefficients. Unlike most known results for sparse recovery, we do not require {\em any} assumption on the matrix other…
Recently, the $\l_{p}$-norm regularization minimization problem $(P_{p}^{\lambda})$ has attracted great attention in compressed sensing. However, the $\l_{p}$-norm $\|x\|_{p}^{p}$ in problem $(P_{p}^{\lambda})$ is nonconvex and…
The paper deals with the problem of finding sparse solutions to systems of polynomial equations possibly perturbed by noise. In particular, we show how these solutions can be recovered from group-sparse solutions of a derived system of…
In this paper, we consider the problem of obtaining the best $k$-sparse solution of $Ax=y$ subject to the constraint that the columns of $A$ are orthogonal. The naive approach for obtaining a solution to this problem has exponential…
This paper studies the copositive optimization problem whose objective is a sparse polynomial, with linear constraints over the nonnegative orthant. We propose sparse Moment-SOS relaxations to solve it. Necessary and sufficient conditions…
This article proposes an efficient numerical method for solving nonlinear partial differential equations (PDEs) based on sparse Gaussian processes (SGPs). Gaussian processes (GPs) have been extensively studied for solving PDEs by…
We consider optimization problems containing nonconvex quadratic functions for which semidefinite programming (SDP) relaxations often yield strong bounds. We investigate linear inequalities that outer approximate the positive semidefinite…
Matrix scaling problems with sparse cost matrices arise frequently in various domains, such as optimal transport, image processing, and machine learning. The Sinkhorn-Knopp algorithm is a popular iterative method for solving these problems,…
Solutions to the linear complementarity problem (LCP) are naturally sparse in many applications such as bimatrix games and portfolio section problems. Despite that it gives rise to the hardness, sparsity makes optimization faster and…
In this paper we study a broad class of structured nonlinear programming (SNLP) problems. In particular, we first establish the first-order optimality conditions for them. Then we propose sequential convex programming (SCP) methods for…