A simple globally convergent algorithm for the nonsmooth nonconvex single source localization problem

DOI10.1007/s10898-017-0545-6zbMath1386.90117OpenAlexW2734809623MaRDI QIDQ1685585

Shoham Sabach, Kobi Zatlawey, Marc Teboulle, D. Russell Luke

Publication date: 14 December 2017

Published in: Journal of Global Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10898-017-0545-6

zbMATH Keywords

alternating minimizationKurdyka-Łojasiewicz propertymethod of multipliersconvergence in semialgebraic optimizationnonsmooth nonconvex minimizationsingle source localization

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Applications of mathematical programming (90C90) Nonconvex programming, global optimization (90C26) Numerical methods based on nonlinear programming (49M37)

Related Items

A numerical study of single source localization algorithms for phaseless inverse scattering problems, Optimization on Spheres: Models and Proximal Algorithms with Computational Performance Comparisons

Uses Software

• SFSDP
• SNLSDP

Cites Work

• Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
• Proximal alternating linearized minimization for nonconvex and nonsmooth problems
• On the convergence of the proximal algorithm for nonsmooth functions involving analytic features
• On gradients of functions definable in o-minimal structures
• From error bounds to the complexity of first-order descent methods for convex functions
• Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized Gauss-Seidel methods
• On the Solution of the GPS Localization and Circle Fitting Problems
• Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Łojasiewicz Inequality
• Iterative Minimization Schemes for Solving the Single Source Localization Problem
• Global Convergence of Splitting Methods for Nonconvex Composite Optimization
• Characterizations of Łojasiewicz inequalities: Subgradient flows, talweg, convexity
• Further Relaxations of the Semidefinite Programming Approach to Sensor Network Localization
• Variational Analysis
• Exact and Approximate Solutions of Source Localization Problems
• Alternating Projections and Douglas-Rachford for Sparse Affine Feasibility
• Exploiting Sparsity in SDP Relaxation for Sensor Network Localization
• Quantitative Convergence Analysis of Iterated Expansive, Set-Valued Mappings
• Least Squares Algorithms for Time-of-Arrival-Based Mobile Location
• The Łojasiewicz Inequality for Nonsmooth Subanalytic Functions with Applications to Subgradient Dynamical Systems
• Convex Analysis