Exploiting Sparsity in SDP Relaxation of Polynomial Optimization Problems

DOI10.1007/978-1-4614-0769-0_18zbMath1334.90107OpenAlexW153356565MaRDI QIDQ2802536

Kojima, Masakazu, Sunyoung Kim

Publication date: 26 April 2016

Published in: International Series in Operations Research & Management Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-1-4614-0769-0_18

zbMATH Keywords

polynomial optimizationstructured sparsitysensor network localization problemssparse SDP relaxation

Mathematics Subject Classification ID

Semidefinite programming (90C22) Applications of mathematical programming (90C90) Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming (90-02)

Related Items

A convergent hierarchy of SDP relaxations for a class of hard robust global polynomial optimization problems

Uses Software

• Matlab
• SDPLIB
• SDPA
• SeDuMi
• SDPT3
• SparsePOP
• GLOBALLib
• SFSDP
• GAMS
• minpack

Cites Work

• Solving semidefinite-quadratic-linear programs using SDPT3
• Matlab
• GLOBALLib
• Exploiting sparsity in linear and nonlinear matrix inequalities via positive semidefinite matrix completion
• An extension of sums of squares relaxations to polynomial optimization problems over symmetric cones
• A note on sparse SOS and SDP relaxations for polynomial optimization problems over symmetric cones
• Correlative sparsity in primal-dual interior-point methods for LP, SDP, and SOCP
• Exploiting sparsity in semidefinite programming via matrix completion. II: Implementation and numerical results
• Sparsity in sums of squares of polynomials
• Global Optimization with Polynomials and the Problem of Moments
• Algorithm 920
• Testing a Class of Methods for Solving Minimization Problems with Simple Bounds on the Variables
• Testing Unconstrained Optimization Software
• Using SeDuMi 1.02, A Matlab toolbox for optimization over symmetric cones
• SDPLIB 1.2, a library of semidefinite programming test problems
• Detecting Global Optimality and Extracting Solutions in GloptiPoly
• Exploiting Sparsity in SDP Relaxation for Sensor Network Localization
• Convergent Relaxations of Polynomial Matrix Inequalities and Static Output Feedback
• Generalized Lagrangian Duals and Sums of Squares Relaxations of Sparse Polynomial Optimization Problems
• Sums of Squares and Semidefinite Program Relaxations for Polynomial Optimization Problems with Structured Sparsity
• Convergent SDP‐Relaxations in Polynomial Optimization with Sparsity
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item