Related papers: Decomposition of arrow type positive semidefinite …

This work proposes a new moment-SOS hierarchy, called CS-TSSOS, for solving large-scale sparse polynomial optimization problems. Its novelty is to exploit simultaneously correlative sparsity and term sparsity by combining advantages of two…

The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…

Seymour's decomposition theorem for regular matroids is a fundamental result with a number of combinatorial and algorithmic applications. In this work we demonstrate how this theorem can be used in the design of parameterized algorithms on…

It is known that problems like Vertex Cover, Feedback Vertex Set and Odd Cycle Transversal are polynomial time solvable in the class of chordal graphs. We consider these problems in a graph that has at most $k$ vertices whose deletion…

Markov Decision Processes (MDPs), as a general-purpose framework, often overlook the benefits of incorporating the causal structure of the transition and reward dynamics. For a subclass of resource allocation problems, we introduce the…

In the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples…

In this paper, we study possible extensions of the main ideas and methods of constrained DC optimization to the case of nonlinear semidefinite programming problems and more general nonlinear and nonsmooth cone constrained optimization…

Sparse matrix operations involve a large number of zero operands which makes most of the operations redundant. The amount of redundancy magnifies when a matrix operation repeatedly executes on sparse data. Optimizing matrix operations for…

Packing and covering semidefinite programs (SDPs) appear in natural relaxations of many combinatorial optimization problems as well as a number of other applications. Recently, several techniques were proposed, that utilize the particular…

A new sparse SOS decomposition algorithm is proposed based on a new sparsity pattern, called cross sparsity patterns. The new sparsity pattern focuses on the sparsity of terms and thus is different from the well-known correlative sparsity…

We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or non-negative, which makes our algorithm suitable for dictionary learning,…

In this paper, we consider convex quadratic optimization problems with indicator variables when the matrix $Q$ defining the quadratic term in the objective is sparse. We use a graphical representation of the support of $Q$, and show that if…

We present a natural generalization of the recent low rank + sparse matrix decomposition and consider the decomposition of matrices into components of multiple scales. Such decomposition is well motivated in practice as data matrices often…

The sparse generalized eigenvalue problem arises in a number of standard and modern statistical learning models, including sparse principal component analysis, sparse Fisher discriminant analysis, and sparse canonical correlation analysis.…

We propose a decomposition framework for the parallel optimization of the sum of a differentiable function and a (block) separable nonsmooth, convex one. The latter term is typically used to enforce structure in the solution as, for…

In this work, we explore the use of operator splitting algorithms for solving regularized structural topology optimization problems. The context is the classical structural design problems (e.g., compliance minimization and compliant…

Optimization decomposition methods are a fundamental tool to develop distributed solution algorithms for large scale optimization problems arising in fields such as machine learning and optimal control. In this paper, we present an…

In this paper, we study the embedded feature selection problem in linear Support Vector Machines (SVMs), in which a cardinality constraint is employed, leading to an interpretable classification model. The problem is NP-hard due to the…

This paper considers the problem of updating the rank-k truncated Singular Value Decomposition (SVD) of matrices subject to the addition of new rows and/or columns over time. Such matrix problems represent an important computational kernel…

Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in machine learning, statistics, bioinformatics, computer vision, as well as signal and image processing. In theory, this problem can…