An inexact bundle variant suited to column generation
type: Item
instance of: scholarly article
title: An inexact bundle variant suited to column generation
zbMATH Open document ID: 1163.65039
published in: Mathematical Programming. Series A. Series B
publication date: 2009-05-04T00:00:00Z
review text: The authors give a bundle method for constrained convex optimization of the form \[ \text{inf\,}f(u),\quad u\in\mathbb{C},\quad h(u)\leq 0, \] where \(\mathbb{C}\) is a simple closed convex set in the Euclidean space, \(f\) is a simple convex real-valued function and \(h\) is also a convex real-valued function. Instead of using penalty functions, it shifts iterates towards feasibility, by way of a Slater point, assumed to be known. The given method is illustrated on a number of cutting-stock problems.
reviewed by: Hans Benker
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 90C27
zbMATH DE Number: 5550536
author: Krzysztof C. Kiwiel
author: Claude Lemaréchal
describes a project that uses: CUTGEN1
MaRDI profile type: Publication
full work available at URL: s10107-007-0187-4
OpenAlex ID: W2091352139
cites work: Cutting Stock Problems
cites work: Non-Euclidean restricted memory level method for large-scale convex optimization
cites work: Very Large-Scale Linear Programming: A Case Study in Combining Interior Point and Simplex Methods
cites work: Comparison of bundle and classical column generation
cites work: Newton's method for convex programming and Tschebyscheff approximation
cites work: Convergence of some algorithms for convex minimization
cites work: Optimal integer solutions to industrial cutting-stock problems. II: Benchmark results
cites work: A Note on Bounding a Class of Linear Programming Problems, Including Cutting Stock Problems
cites work: Solving semidefinite quadratic problems within nonsmooth optimization algorithms
cites work: CUTGEN1: A problem generator for the standard one-dimensional cutting stock problem
cites work: A Linear Programming Approach to the Cutting-Stock Problem
cites work: A proximal bundle method based on approximate subgradients
cites work: Q3141900
cites work: A bundle-filter method for nonsmooth convex constrained optimization
cites work: The Cutting-Plane Method for Solving Convex Programs
cites work: An Algorithm for Nonsmooth Convex Minimization With Errors
cites work: Methods of descent for nondifferentiable optimization
cites work: A constraint linearization method for nondifferentiable convex minimization
cites work: Exact penalty functions in proximal bundle methods for constrained convex nondifferentiable minimization
cites work: A Cholesky dual method for proximal piecewise linear programming
cites work: Approximations in proximal bundle methods and decomposition of convex programs
cites work: Finding normal solutions in piecewise linear programming
cites work: Proximal level bundle methods for convex nondifferentiable optimization, saddle-point problems and variational inequalities
cites work: An inexact bundle approach to cutting-stock problems
cites work: A Proximal Bundle Method with Approximate Subgradient Linearizations
cites work: A Proximal‐Projection Bundle Method for Lagrangian Relaxation, Including Semidefinite Programming
cites work: Q4735938
cites work: New variants of bundle methods
cites work: Selected Topics in Column Generation
cites work: A Column Generation Approach for Graph Coloring
cites work: An Algorithm for Constrained Optimization with Semismooth Functions
cites work: Convex Analysis
cites work: An Infeasible Bundle Method for Nonsmooth Convex Constrained Optimization without a Penalty Function or a Filter
cites work: A Branch-and-Price Algorithm for the Generalized Assignment Problem
cites work: On approximations with finite precision in bundle methods for nonsmooth optimization
cites work: Computational study of a column generation algorithm for bin packing and cutting stock problems
cites work: On Dantzig-Wolfe Decomposition in Integer Programming and ways to Perform Branching in a Branch-and-Price Algorithm
cites work: Heuristics for the integer one-dimensional cutting stock problem: A computational study
cites work: Q4254875
DOI: 10.1007/S10107-007-0187-4
description: scientific article; zbMATH DE number 5550536