Algorithm 813: SPG—Software for Convex-Constrained Optimization
ACM Transactions on Mathematical Software (TOMS)
Nonmonotone Spectral Projected Gradient Methods on Convex Sets
SIAM Journal on Optimization
Large-Scale Active-Set Box-Constrained Optimization Method with Spectral Projected Gradients
Computational Optimization and Applications
Reformulation descent applied to circle packing problems
Computers and Operations Research
Numerical Comparison of Augmented Lagrangian Algorithms for Nonconvex Problems
Computational Optimization and Applications
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Minimax optimal placement problem for special-form objects on a multiply connected domain
Cybernetics and Systems Analysis
Minimizing the object dimensions in circle and sphere packing problems
Computers and Operations Research
Cutting circles and polygons from area-minimizing rectangles
Journal of Global Optimization
Hybrid spectral gradient method for the unconstrained minimization problem
Journal of Global Optimization
Computers and Operations Research
Mathematical model and efficient algorithms for object packing problem
Computational Geometry: Theory and Applications
Orthogonal packing of identical rectangles within isotropic convex regions
Computers and Industrial Engineering
A heuristic approach for packing identical rectangles in convex regions
Computers and Operations Research
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The orthogonal packing of rectangular items in an arbitrary convex region is considered in this work. The packing problem is modeled as the problem of deciding for the feasibility or infeasibility of a set of nonlinear equality and inequality constraints. A procedure based on nonlinear programming is introduced and numerical experiments which show that the new procedure is reliable are exhibited.Scope and purpose We address the problem of packing orthogonal rectangles within an arbitrary convex region. We aim to show that smooth nonlinear programming models are a reliable alternative for packing problems and that well-known general-purpose methods based on continuous optimization can be used to solve the models. Numerical experiments illustrate the capabilities and limitations of the approach.