## ACCPM - A Library for Convex Optimization Based on an Analytic Center Cutting Plane Method (1996)

Venue: | European Journal of Operational Research |

Citations: | 35 - 17 self |

### BibTeX

@ARTICLE{Gondzio96accpm-,

author = {J. Gondzio and O. Du Merle and R. Sarkissian and J. -p. Vial},

title = {ACCPM - A Library for Convex Optimization Based on an Analytic Center Cutting Plane Method},

journal = {European Journal of Operational Research},

year = {1996},

volume = {94},

pages = {206--211}

}

### Years of Citing Articles

### OpenURL

### Abstract

Introduction We are concerned in this note with the Goffin Haurie and Vial's [7] Analytic Center Cutting Plane Method (ACCPM for short) for large-scale convex optimization. Its state-of-the-art implementation [10] is now available upon request for academic research use. Cutting plane methods for convex optimization have a long history that goes back at least to a fundamental paper of Kelley [14]. There exist numerous strategies that can be applied to "solve" subsequent relaxed master problems in the cutting planes optimization scheme. In the Analytic Center Cutting Plane Method, subsequent relaxed master problems are not solved to optimality. Instead of it, an approximate analytic center of the current localization set is looked for. The theoretical development of ACCPM started from Goffin and Vial [9]. It was later continued in [7, 8] and led to a development of the prototype implementation of the method due to du Merle [15] that was successfully applied to solve several nont

### Citations

446 |
LAPACK Usersâ€™ Guide
- Anderson, Bai, et al.
- 1995
(Show Context)
Citation Context ...es. Installation of ACCPM ACCPM library is written in C++. An exception are the Cholesky factorization routines written in FORTRAN 77: the sparse one due to Gondzio [11] and the dense one from LAPACK =-=[1]-=-. The library and examples of its application are placed in a directory accpm. This directory contains a read.me file, a PostScript version of the most recent revision of ACCPM's user's guide, useaccp... |

120 |
The cutting plane method for solving convex programs
- KELLEY
- 1960
(Show Context)
Citation Context ...implementation [10] is now available upon request for academic research use. Cutting plane methods for convex optimization have a long history that goes back at least to a fundamental paper of Kelley =-=[14]. There ex-=-ist numerous strategies that can be applied to "solve" subsequent relaxed master problems in the cutting planes optimization scheme. In the Analytic Center Cutting Plane Method, subsequent r... |

117 |
The decomposition algorithm for linear programming
- Danzig, Wolfe
- 1961
(Show Context)
Citation Context ... l j ; yisoe l j ; 8l 2sfsb ; j = 1; : : : ; p: (12) Analytic center There exists a number of possible strategies that can be applied at step 1 of the cutting plane method. The optimal point strategy =-=[4], for exam-=-ple, consists in solving every relaxed master program (7) to optimality. The central point strategy [9] consists in finding some "central point" in a localization set. The discussion of thei... |

71 |
Decomposition and nondifferentiable optimization with the projective algorithm
- Goffin, A, et al.
- 1992
(Show Context)
Citation Context ... center. Hardware information: Any computer with C++ and FORTRAN 77 compilers. Software information: C++ and FORTRAN 77. 1 Introduction We are concerned in this note with the Goffin Haurie and Vial's =-=[7]-=- Analytic Center Cutting Plane Method (ACCPM for short) for large-scale convex optimization. Its state-of-the-art implementation [10] is now available upon request for academic research use. Cutting p... |

52 | A cutting plane method from analytic centers for stochastic programming
- Bahn, Merle, et al.
- 1995
(Show Context)
Citation Context ... continued in [7, 8] and led to a development of the prototype implementation of the method due to du Merle [15] that was successfully applied to solve several nontrivial convex optimization problems =-=[2, 3]-=-. This research has been supported by the Fonds National de la Recherche Scientifique Suisse, grant #12 \Gamma 34002:92. y to appear in European Journal of Operational Research. z on leave from the Sy... |

39 | Solving nonlinear multicommodity flow problems by the analytic center cutting plane method
- Goffin, Gondzio, et al.
- 1997
(Show Context)
Citation Context ...ropean Journal of Operational Research. z on leave from the Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447 Warsaw, Poland. A need to solve very large optimization problems =-=[6]-=- motivated us to rewrite the program from scratch so as to make it more flexible and easier to use for the general convex optimization problems. The new implementation of the method due to Gondzio, du... |

25 |
A polynomial Newton method for linear programming
- Ghellinck, Vial
- 1986
(Show Context)
Citation Context ...nition of L does not change the geometry of the polytope, but it does change its analytic center --- the repeated constraint moves the analytic center away.) ACCPM employs the de Ghellinck and Vial's =-=[5]-=- potential reduction algorithm to find an analytic center of the current localization set. 3 How to use ACCPM We are aware that ACCPM represents a fairly complicated optimization technique. Hence to f... |

21 |
Cutting Planes and Column Generation Techniques with the Projective Agorithm
- Goffin, Vial
- 1990
(Show Context)
Citation Context ...r problems are not solved to optimality. Instead of it, an approximate analytic center of the current localization set is looked for. The theoretical development of ACCPM started from Goffin and Vial =-=[9]-=-. It was later continued in [7, 8] and led to a development of the prototype implementation of the method due to du Merle [15] that was successfully applied to solve several nontrivial convex optimiza... |

16 | A computational view of interior-point methods for linear programming
- Gondzio, Terlaky
- 1996
(Show Context)
Citation Context ...rm of a callable library libaccpm.a. 2 Fundamentals of ACCPM The algorithm implemented in ACCPM combines two powerful optimization techniques: cutting plane methods [14] and interior point algorithms =-=[13, 17]-=-. Its detailed description is definitely beyond the scope of this short note. The reader interested in the theory and the implementation details should consult [10] and the references therein. We shal... |

13 | Using an interior point method for the master problem in a decomposition approach
- Goffin, Sarkissian, et al.
- 1997
(Show Context)
Citation Context ...e general convex optimization problems. The new implementation of the method due to Gondzio, du Merle, Sarkissian and Vial [10] responds these needs. All recent theoretical and practical developments =-=[16, 12]-=- have been incorporated into it, resulting in the creation of a sophisticated optimization tool. We now make it available to the user, in the form of a callable library libaccpm.a. 2 Fundamentals of A... |

12 |
Using central prices in the decomposition of linear programs
- Goffin, Haurie, et al.
- 1993
(Show Context)
Citation Context ...timality. Instead of it, an approximate analytic center of the current localization set is looked for. The theoretical development of ACCPM started from Goffin and Vial [9]. It was later continued in =-=[7, 8]-=- and led to a development of the prototype implementation of the method due to du Merle [15] that was successfully applied to solve several nontrivial convex optimization problems [2, 3]. This researc... |

12 | On the Comparative Behavior of Kelley's Cutting Plane Method and the Analytic Center Cutting Plane Method
- Merle, Goffin, et al.
- 1996
(Show Context)
Citation Context ...e general convex optimization problems. The new implementation of the method due to Gondzio, du Merle, Sarkissian and Vial [10] responds these needs. All recent theoretical and practical developments =-=[16, 12]-=- have been incorporated into it, resulting in the creation of a sophisticated optimization tool. We now make it available to the user, in the form of a callable library libaccpm.a. 2 Fundamentals of A... |

8 |
Implementing Cholesky factorization for interior point niethods of linear programming,'' Optirnizution 27
- Gondzio
- 1993
(Show Context)
Citation Context ...cpm.a library and follow the examples. Installation of ACCPM ACCPM library is written in C++. An exception are the Cholesky factorization routines written in FORTRAN 77: the sparse one due to Gondzio =-=[11]-=- and the dense one from LAPACK [1]. The library and examples of its application are placed in a directory accpm. This directory contains a read.me file, a PostScript version of the most recent revisio... |

5 |
Experimental behaviour of an interior point cutting plane algorithm for convex programming: an application to geometric programming, Discrete Applied Mathematics 49
- Bahn, Goffin, et al.
- 1994
(Show Context)
Citation Context ... continued in [7, 8] and led to a development of the prototype implementation of the method due to du Merle [15] that was successfully applied to solve several nontrivial convex optimization problems =-=[2, 3]-=-. This research has been supported by the Fonds National de la Recherche Scientifique Suisse, grant #12 \Gamma 34002:92. y to appear in European Journal of Operational Research. z on leave from the Sy... |

2 |
An advanced implementation of the analytic center cutting plane method and its applications
- Gondzio, Merle, et al.
- 1995
(Show Context)
Citation Context ...ion We are concerned in this note with the Goffin Haurie and Vial's [7] Analytic Center Cutting Plane Method (ACCPM for short) for large-scale convex optimization. Its state-of-the-art implementation =-=[10]-=- is now available upon request for academic research use. Cutting plane methods for convex optimization have a long history that goes back at least to a fundamental paper of Kelley [14]. There exist n... |

2 |
Interior Points and Cutting Palnes: a Development and Implementation of Methods for Convex Optimization and Large Scale Structured Linear Programming
- du
- 1995
(Show Context)
Citation Context ...ked for. The theoretical development of ACCPM started from Goffin and Vial [9]. It was later continued in [7, 8] and led to a development of the prototype implementation of the method due to du Merle =-=[15]-=- that was successfully applied to solve several nontrivial convex optimization problems [2, 3]. This research has been supported by the Fonds National de la Recherche Scientifique Suisse, grant #12 \G... |