Global optimization approach to unequal global optimization approach to unequal sphere packing problems in 3D

DOI10.1023/A:1016083231326zbMath1026.90078OpenAlexW988732486MaRDI QIDQ1862200

Yanyan Li

Publication date: 10 March 2003

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1016083231326

zbMATH Keywords

nonconvex quadratic programmingheuristic algorithmsLP relaxationsimplicial branch-and-bound algorithmunequal sphere packing problem

Mathematics Subject Classification ID

Nonconvex programming, global optimization (90C26) Approximation methods and heuristics in mathematical programming (90C59) Combinatorial optimization (90C27)

Related Items (25)

A local search-based method for sphere packing problems ⋮ Modeling close packing of 3D objects ⋮ Packing unequal spheres into various containers ⋮ Stability and convergence analysis of a dynamics-based collective method for random sphere packing ⋮ Experimental Design Problems and Nash Equilibrium Solutions ⋮ Covering a convex 3D polytope by a minimal number of congruent spheres ⋮ A literature review on circle and sphere packing problems: models and methodologies ⋮ Linearization of Euclidean norm dependent inequalities applied to multibeam satellites design ⋮ Using general triangle inequalities within quadratic convex reformulation method ⋮ New bounds for nonconvex quadratically constrained quadratic programming ⋮ Digital model of natural cores using geometric design ⋮ A new semidefinite programming relaxation scheme for a class of quadratic matrix problems ⋮ Packing identical spheres into a cylinder ⋮ Optimized packing multidimensional hyperspheres: a unified approach ⋮ The discrete ellipsoid covering problem: a discrete geometric programming approach ⋮ Advances in particle packing algorithms for generating the medium in the discrete element method ⋮ Packing congruent spheres into a multi‐connected polyhedral domain ⋮ Generation of tetrahedral mesh of variable element size by sphere packing over an unbounded 3D domain ⋮ Semidefinite relaxations for quadratically constrained quadratic programming: A review and comparisons ⋮ Optimal configuration of gamma ray machine radiosurgery units: The sphere covering subproblem ⋮ Packing cylinders and rectangular parallelepipeds with distances between them into a given region ⋮ Optimized filling of a given cuboid with spherical powders for additive manufacturing ⋮ GREEDY ALGORITHMS FOR PACKING UNEQUAL SPHERES INTO A CUBOIDAL STRIP OR A CUBOID ⋮ Monte Carlo study of the sphere packing problem ⋮ Constraints in container loading -- a state-of-the-art review

Uses Software

• Global Optimization Toolbox For Maple

Cites Work

• A global optimization algorithm for polynomial programming problems using a reformulation-linearization technique
• A simplicial branch-and-bound method for solving nonconvex all-quadratic programs
• Handbook of global optimization
• A relaxation method for nonconvex quadratically constrained quadratic programs
• Packing of unequal spheres and automated radiosurgical treatment planning
• On generalized bisection of 𝑛-simplices
• On Three-Dimensional Packing
• A Strip-Packing Algorithm with Absolute Performance Bound 2

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