Computing the nearest Euclidean distance matrix with low embedding dimensions

DOI10.1007/s10107-013-0726-0zbMath1304.49051OpenAlexW2007304358MaRDI QIDQ463737

Hou-Duo Qi, Xiao-Ming Yuan

Publication date: 17 October 2014

Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)

Full work available at URL: https://eprints.soton.ac.uk/361847/1/EDM_Embedding_Final.pdf

zbMATH Keywords

low-rank approximationsemismooth Newton-CG methodEuclidean distance matrixLagrangian dualitymajorization method

Mathematics Subject Classification ID

Convex programming (90C25) Newton-type methods (49M15) Numerical methods based on nonlinear programming (49M37) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33)

Related Items (22)

An inexact proximal DC algorithm with sieving strategy for rank constrained least squares semidefinite programming ⋮ Regularity properties of non-negative sparsity sets ⋮ Convex Euclidean distance embedding for collaborative position localization with NLOS mitigation ⋮ Model-based distance embedding with applications to chromosomal conformation biology ⋮ An Ordinal Weighted EDM Model for Nonmetric Multidimensional Scaling ⋮ Feasibility and a fast algorithm for Euclidean distance matrix optimization with ordinal constraints ⋮ A facial reduction approach for the single source localization problem ⋮ Perturbation analysis of the Euclidean distance matrix optimization problem and its numerical implications ⋮ Ordinal Distance Metric Learning with MDS for Image Ranking ⋮ An efficient augmented Lagrangian method for support vector machine ⋮ Robust Euclidean embedding via EDM optimization ⋮ A multi-stage convex relaxation approach to noisy structured low-rank matrix recovery ⋮ Noisy Euclidean distance matrix completion with a single missing node ⋮ Quartic first-order methods for low-rank minimization ⋮ Matrix optimization based Euclidean embedding with outliers ⋮ Regularized multidimensional scaling with radial basis functions ⋮ A Euclidean distance matrix model for protein molecular conformation ⋮ Discriminant analysis of regularized multidimensional scaling ⋮ The Analytic Solutions of a Class of Constrained Matrix Minimization and Maximization Problems with Applications ⋮ A Convex Matrix Optimization for the Additive Constant Problem in Multidimensional Scaling with Application to Locally Linear Embedding ⋮ Constrained Best Euclidean Distance Embedding on a Sphere: A Matrix Optimization Approach ⋮ On Optimality Conditions for Nonlinear Conic Programming

Uses Software

• SFSDP
• SNLSDP

Cites Work

• Explicit Sensor Network Localization using Semidefinite Representations and Facial Reductions
• Properties of Euclidean and non-Euclidean distance matrices
• Approximation by matrices positive semidefinite on a subspace
• A successive projection method
• Connections between the real positive semidefinite and distance matrix completion problems
• Recent advances on the discretizable molecular distance geometry problem
• Euclidean Distance Matrices and Applications
• Solving Nuclear Norm Regularized and Semidefinite Matrix Least Squares Problems with Linear Equality Constraints
• An Inexact Accelerated Proximal Gradient Method for Large Scale Linearly Constrained Convex SDP
• Exploiting Sparsity in SDP Relaxation for Sensor Network Localization
• Unnamed Item

This page was built for publication: Computing the nearest Euclidean distance matrix with low embedding dimensions