Convex relaxation and variational approximation of the Steiner problem: theory and numerics

DOI10.1515/geofl-2018-0003zbMath1393.49006OpenAlexW2795892747MaRDI QIDQ1647911

Mauro Bonafini

Publication date: 27 June 2018

Published in: Geometric Flows (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/geofl-2018-0003

zbMATH Keywords

calculus of variationsconvex relaxation\(\Gamma\)-convergencegeometric measure theorySteiner's tree problem

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Variational problems in a geometric measure-theoretic setting (49Q20) Planar graphs; geometric and topological aspects of graph theory (05C10) Steiner systems in finite geometry (51E10) Methods involving semicontinuity and convergence; relaxation (49J45) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Numerical methods of relaxation type (49M20)

Related Items (5)

Optimal synchronization problem for a multi-agent system ⋮ The oriented mailing problem and its convex relaxation ⋮ Calibrations for minimal networks in a covering space setting ⋮ On different notions of calibrations for minimal partitions and minimal networks in \(\mathbb{R}^2\) ⋮ A Multimaterial Transport Problem and its Convex Relaxation via Rectifiable $G$-currents

Uses Software

• KNITRO
• Mosek
• JuMP

Cites Work

• Unnamed Item
• A Modica-Mortola approximation for branched transport and applications
• The Steiner tree problem revisited through rectifiable \(G\)-currents
• On a phase field approximation of the planar Steiner problem: existence, regularity, and asymptotic of minimizers
• Geometric measure theory.
• An optimal irrigation network with infinitely many branching points
• A Convex Approach to Minimal Partitions
• Approximation of Length Minimization Problems Among Compact Connected Sets
• JuMP: A Modeling Language for Mathematical Optimization

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