相关论文: Exploiting Sparsity in Complex Polynomial Optimiza…

The Sum-of-Squares (SoS) hierarchy of semidefinite programs is a powerful algorithmic paradigm which captures state-of-the-art algorithmic guarantees for a wide array of problems. In the average case setting, SoS lower bounds provide strong…

Recently several methods were proposed for sparse optimization which make careful use of second-order information [10, 28, 16, 3] to improve local convergence rates. These methods construct a composite quadratic approximation using Hessian…

We study several questions related to diversifying search results. We give improved approximation algorithms in each of the following problems, together with some lower bounds. - We give a polynomial-time approximation scheme (PTAS) for a…

In this paper, we propose a general framework to design {efficient} polynomial time approximation schemes (EPTAS) for fundamental stochastic combinatorial optimization problems. Given an error parameter $\epsilon>0$, such algorithmic…

Decoders are a critical component of fault-tolerant quantum computing. They must identify errors based on syndrome measurements to correct quantum states. While finding the optimal correction is NP-hard and thus extremely difficult,…

We study sparsity in the max-plus algebraic setting. We seek both exact and approximate solutions of the max-plus linear equation with minimum cardinality of support. In the former case, the sparsest solution problem is shown to be…

The LASSO is an attractive regularisation method for linear regression that combines variable selection with an efficient computation procedure. This paper is concerned with enhancing the performance of LASSO for square-free hierarchical…

In this paper, to solve a broad class of complex symmetric linear systems, we recast the complex system in a real formulation and apply the generalized successive overrelaxation (GSOR) iterative method to the equivalent real system. We then…

The moment-SOS hierarchy is a widely applicable framework to address polynomial optimization problems over basic semi-algebraic sets based on positivity certificates of polynomial. Recent works show that the convergence rate of this…

This article details the algorithmics in FLSSS, an R package for solving various subset sum problems. The fundamental algorithm engages the problem via combinatorial space compression adaptive to constraints, relaxations and variations that…

We give new algorithms based on the sum-of-squares method for tensor decomposition. Our results improve the best known running times from quasi-polynomial to polynomial for several problems, including decomposing random overcomplete…

We consider the problem of sparse atomic optimization, where the notion of "sparsity" is generalized to meaning some linear combination of few atoms. The definition of atomic set is very broad; popular examples include the standard basis,…

An algorithm is proposed for solving optimization problems arising in neural network training for supervised learning. The unique feature of the algorithm is the use of an auxiliary loss, in addition to the original loss employed for model…

We identify a new sufficient condition for the finite convergence of moment relaxations of polynomial optimization problems with correlative sparsity. This condition, which follows from a solution to a correlatively sparse version of the…

In order to improve the performance of Least Mean Square (LMS) based system identification of sparse systems, a new adaptive algorithm is proposed which utilizes the sparsity property of such systems. A general approximating approach on…

The constrained zonotope is a polytopic set representation widely used for set-based analysis and control of dynamic systems. This paper develops methods to formulate and solve optimization problems for dynamic systems in real time using…

Constraint satisfaction problem (CSP) has been actively used for modeling and solving a wide range of complex real-world problems. However, it has been proven that developing efficient methods for solving CSP, especially for large problems,…

We study planted problems---finding hidden structures in random noisy inputs---through the lens of the sum-of-squares semidefinite programming hierarchy (SoS). This family of powerful semidefinite programs has recently yielded many new…

Matroid intersection is a classical optimization problem where, given two matroids over the same ground set, the goal is to find the largest common independent set. In this paper, we show that there exists a certain "sparsifer": a subset of…

In this article, we design and analyze a hybrid high-order (HHO) finite element approximation for the solution of a nonlocal nonlinear problem of Kirchhoff type. The HHO method involves arbitrary-order polynomial approximations on…