Computing tight bounds via piecewise linear functions through the example of circle cutting problems

DOI10.1007/s00186-016-0546-0zbMath1396.90051OpenAlexW2439104872MaRDI QIDQ328518

Steffen Rebennack

Publication date: 20 October 2016

Published in: Mathematical Methods of Operations Research (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00186-016-0546-0

zbMATH Keywords

global optimizationinner approximationouter approximationnonlinear programmingmixed integer linear programmingnon-convex optimizationpiecewise linear functionscircle cuttingincremental formulationlogarithmic formulationquadratically constrained programming

Mathematics Subject Classification ID

Mixed integer programming (90C11) Nonconvex programming, global optimization (90C26) Nonlinear programming (90C30) Linear programming (90C05) Approximation methods and heuristics in mathematical programming (90C59)

Related Items (10)

Sequence of polyhedral relaxations for nonlinear univariate functions ⋮ A Comparison of Two Mixed-Integer Linear Programs for Piecewise Linear Function Fitting ⋮ Data-driven mixed-integer linear programming-based optimisation for efficient failure detection in large-scale distributed systems ⋮ A linear programming approach to difference-of-convex piecewise linear approximation ⋮ Two-stage stochastic mixed-integer nonlinear programming model for post-wildfire debris flow hazard management: mitigation and emergency evacuation ⋮ An effective logarithmic formulation for piecewise linearization requiring no inequality constraint ⋮ On tackling reverse convex constraints for non-overlapping of unequal circles ⋮ Piecewise Linear Function Fitting via Mixed-Integer Linear Programming ⋮ Data-driven stochastic optimization for distributional ambiguity with integrated confidence region ⋮ Non-convex nested Benders decomposition

Uses Software

• MIPLIB
• GAMS
• ANTIGONE

Cites Work

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