Related papers: A Quadratic Penalty Method for Hypergraph Matching

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel…

Sparsity constrained minimization captures a wide spectrum of applications in both machine learning and signal processing. This class of problems is difficult to solve since it is NP-hard and existing solutions are primarily based on…

We consider a linear inverse problem whose solution is expressed as a sum of two components: one smooth and the other sparse. This problem is addressed by minimizing an objective function with a least squares data-fidelity term and a…

Mean-reverting portfolios with few assets, but high variance, are of great interest for investors in financial markets. Such portfolios are straightforwardly profitable because they include a small number of assets whose prices not only…

A hypergraph is a generalization of a graph, in which a hyperedge can connect multiple vertices, modeling complex relationships involving multiple vertices simultaneously. Hypergraph pattern matching, which is to find all isomorphic…

In high-dimensional statistics, variable selection recovers the latent sparse patterns from all possible covariate combinations. This paper proposes a novel optimization method to solve the exact L0-regularized regression problem, which is…

Sparse Gaussian graphical models characterize sparse dependence relationships between random variables in a network. To estimate multiple related Gaussian graphical models on the same set of variables, we formulate a hierarchical model,…

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…

This paper focuses on the design of sequential quadratic optimization (commonly known as SQP) methods for solving large-scale nonlinear optimization problems. The most computationally demanding aspect of such an approach is the computation…

We consider the densest $k$-subgraph problem, which seeks to identify the $k$-node subgraph of a given input graph with maximum number of edges. This problem is well-known to be NP-hard, by reduction to the maximum clique problem. We…

A new exact projective penalty method is proposed for the equivalent reduction of constrained optimization problems to nonsmooth unconstrained ones. In the method, the original objective function is extended to infeasible points by summing…

The non-negative solution to an underdetermined linear system can be uniquely recovered sometimes, even without imposing any additional sparsity constraints. In this paper, we derive conditions under which a unique non-negative solution for…

Learning processes are useful methodologies able to improve knowledge of real phenomena. These are often dependent on hyperparameters, variables set before the training process and regulating the learning procedure. Hyperparameters…

Spreading the information over all coefficients of a representation is a desirable property in many applications such as digital communication or machine learning. This so-called antisparse representation can be obtained by solving a convex…

We propose a novel optimization-based approach to embedding heterogeneous high-dimensional data characterized by a graph. The goal is to create a two-dimensional visualization of the graph structure such that edge-crossings are minimized…

In this paper we propose a global optimization-based approach to jointly matching a set of images. The estimated correspondences simultaneously maximize pairwise feature affinities and cycle consistency across multiple images. Unlike…

This paper investigates simple bilevel optimization problems where we minimize an upper-level objective over the optimal solution set of a convex lower-level objective. Existing methods for such problems either only guarantee asymptotic…

This paper proposes a new algorithm for simultaneous graph matching and clustering. For the first time in the literature, these two problems are solved jointly and synergetically without relying on any training data, which brings advantages…

Graph matching aims to find correspondences between two graphs. This paper integrates several well-known graph matching algorithms into a framework: the constrained gradient method. The primary difference among these algorithms lies in…

In 2016, Chandrasekaran, V\'egh, and Vempala published a method to solve the minimum-cost perfect matching problem on an arbitrary graph by solving a strictly polynomial number of linear programs. However, their method requires a strong…