Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Branch-and-Price Algorithms for the One-Dimensional Cutting Stock Problem
Computational Optimization and Applications
Dual Applications of Proximal Bundle Methods, Including Lagrangian Relaxation of Nonconvex Problems
SIAM Journal on Optimization
Optimal Integer Solutions to Industrial Cutting Stock Problems
INFORMS Journal on Computing
Optimal Integer Solutions to Industrial Cutting-Stock Problems: Part 2, Benchmark Results
INFORMS Journal on Computing
Using Extra Dual Cuts to Accelerate Column Generation
INFORMS Journal on Computing
A Proximal Bundle Method with Approximate Subgradient Linearizations
SIAM Journal on Optimization
Setup and Open-Stacks Minimization in One-Dimensional Stock Cutting
INFORMS Journal on Computing
A Proximal-Projection Bundle Method for Lagrangian Relaxation, Including Semidefinite Programming
SIAM Journal on Optimization
Comparison of bundle and classical column generation
Mathematical Programming: Series A and B
An inexact bundle variant suited to column generation
Mathematical Programming: Series A and B
Level bundle methods for constrained convex optimization with various oracles
Computational Optimization and Applications
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We show that the linear programming relaxation of the cutting-stock problem can be solved efficiently by the recently proposed inexact bundle method. This method saves work by allowing inaccurate solutions to knapsack subproblems. With suitable rounding heuristics, our method solves almost all the cutting-stock instances from the literature.