相关论文: Exploiting term sparsity in Noncommutative Polynom…

In the field of uncertainty quantification, sparse polynomial chaos (PC) expansions are commonly used by researchers for a variety of purposes, such as surrogate modeling. Ideas from compressed sensing may be employed to exploit this…

Sparsity, which occurs in both scientific applications and Deep Learning (DL) models, has been a key target of optimization within recent ASIC accelerators due to the potential memory and compute savings. These applications use data stored…

In this paper, we investigate optimization problems with nonnegative and orthogonal constraints, where any feasible matrix of size $n \times p$ exhibits a sparsity pattern such that each row accommodates at most one nonzero entry. Our…

Among many approaches to increase the computational efficiency of semidefinite programming (SDP) relaxation for quadratic constrained quadratic programming problems (QCQPs), exploiting the aggregate sparsity of the data matrices in the SDP…

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…

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…

Large-scale non-convex sparsity-constrained problems have recently gained extensive attention. Most existing deterministic optimization methods (e.g., GraSP) are not suitable for large-scale and high-dimensional problems, and thus…

Sparsity promoting norms are frequently used in high dimensional regression. A limitation of such Lasso-type estimators is that the optimal regularization parameter depends on the unknown noise level. Estimators such as the concomitant…

Recent research has shown that performance in signal processing tasks can often be significantly improved by using signal models based on sparse representations, where a signal is approximated using a small number of elements from a fixed…

In sparse optimization, enforcing hard constraints using the $\ell_0$ pseudo-norm offers advantages like controlled sparsity compared to convex relaxations. However, many real-world applications demand not only sparsity constraints but also…

Sparsity is a ubiquitous feature of many real world signals such as natural images and neural spiking activities. Conventional compressed sensing utilizes sparsity to recover low dimensional signal structures in high ambient dimensions…

Non-commutative polynomial optimization (NPO) problems seek to minimize the state average of a polynomial of some operator variables, subject to polynomial constraints, over all states and operators, as well as the Hilbert spaces where…

Motivated by recent progress in quantum information theory, this article aims at optimizing trace polynomials, i.e., polynomials in noncommuting variables and traces of their products. A novel Positivstellensatz certifying positivity of…

Automated code generation and performance enhancements for sparse tensor algebra have become essential in many real-world applications, such as quantum computing, physical simulations, computational chemistry, and machine learning. General…

Finding the sparsest solutions to a tensor complementarity problem is generally NP-hard due to the nonconvexity and noncontinuity of the involved $\ell_0$ norm. In this paper, a special type of tensor complementarity problems with…

In exact sparse optimization problems on Rd (also known as sparsity constrained problems), one looks for solution that have few nonzero components. In this paper, we consider problems where sparsity is exactly measured either by the…

Sparse Optimal Scoring (SOS) reformulates linear discriminant analysis to enable feature selection through elastic net regularization, making it well-suited for high-dimensional settings where the number of features exceeds observations.…

This paper studies how to solve semi-infinite polynomial programming (SIPP) problems by semidefinite relaxation method. We first introduce two SDP relaxation methods for solving polynomial optimization problems with finitely many…

We consider sparsity-based techniques for the approximation of high-dimensional functions from random pointwise evaluations. To date, almost all the works published in this field contain some a priori assumptions about the error corrupting…

This paper proposes tight semidefinite relaxations for polynomial optimization. The optimality conditions are investigated. We show that generally Lagrange multipliers can be expressed as polynomial functions in decision variables over the…