A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2007; you can also visit the original URL.
The file type is application/pdf.
Filters
Towards a practical parallelisation of the simplex method
2008
Computational Management Science
Preserved Fulltext
This paper reviews previous attempts to parallelise the simplex method in relation to efficient serial simplex techniques and the nature of practical LP problems. ...
For the major challenge of solving general large sparse LP problems, there has been no parallelisation of the simplex method that offers significantly improved performance over a good serial implementation ...
As a consequence, although work on parallelising the simplex method using dense matrix algebra has generally exploited data parallelism, it was a commonly held view that when using sparse matrix algebra ...
doi:10.1007/s10287-008-0080-5
fatcat:7rdsk7ic7bca7dy5e6yvybuioq
Minimum volume simplicial enclosure for spectral unmixing of remotely sensed hyperspectral data
2010
2010 IEEE International Geoscience and Remote Sensing Symposium
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
In order to interpret the results in Table 1 , let us first focus on the scene with opaque trees and sparse population (CASI01 01). ...
Canopies of both opaque and translucent trees were designed with sparse and dense populations. ...
doi:10.1109/igarss.2010.5649694
dblp:conf/igarss/HendrixGPP10
fatcat:45jkjjml55d7ha3novwhdseez4
GPU Acceleration of the Matrix-Free Interior Point Method
[chapter]
2012
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2014; you can also visit the original URL.
The file type is application/pdf.
The matrix-free method is one such approach and is so named since the iterative solution procedure requires only the results of operations Ax and A T y, where A is the matrix of constraint coefficients ...
Since the computational cost of these operations may well dominate the total solution time for the problem, it is important that the techniques used to perform them are efficient. ...
Its focus on a small core of sparse operations makes highly optimized implementations using state of the art hardware possible without excessive difficulty. ...
doi:10.1007/978-3-642-31464-3_69
fatcat:3klpdqf55vawpigj7wdcag7fla
Parallelizing the dual revised simplex method
2017
Mathematical Programming Computation
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
One of the authors has implemented the techniques underlying PAMI within the FICO Xpress simplex solver and this paper presents computational results demonstrating their value. ...
This paper introduces the design and implementation of two parallel dual simplex solvers for general large scale sparse linear programming problems. ...
For many sparse LP problems the matrix B −1 is dense, so solutions of linear systems involving B or B T can be expected to be dense even when, as is typically the case in the revised simplex method, the ...
doi:10.1007/s12532-017-0130-5
fatcat:7l3elmcu2jg4ffeswgq4oqlywq
Parallelizing the dual revised simplex method
[article]
2015
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
One of the authors has implemented the techniques underlying PAMI within the FICO Xpress simplex solver and this paper presents computational results demonstrating their value. ...
This paper introduces the design and implementation of two parallel dual simplex solvers for general large scale sparse linear programming problems. ...
For many sparse LP problems the matrix B −1 is dense, so solutions of linear systems involving B or B T can be expected to be dense even when, as is typically the case in the revised simplex method, the ...
arXiv:1503.01889v1
fatcat:dp3migoocjd35ou7bmg7yd3v3y
Implementing interior point linear programming methods in the Optimization Subroutine Library
1992
IBM Systems Journal
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2006; you can also visit the original URL.
The file type is application/pdf.
This class of methods uses quite different computational kernels than the traditional simplex method. ...
In particular, interior methods can benefit greatly from use of vector architectures on the IBM 3090'" series computers and "super-scalar" processing on the RlSC System/6000" series. s . = x . ...
Acknowledgments We are indebted to Jenny Edwards for converting the ESSLl6000 dense Cholesky routines to function under OSL, to Fred Gustavson for helpful discussions, and to Irvin Lustig for generating ...
doi:10.1147/sj.311.0026
fatcat:kpcxuhvq6fd45ojhsx4vcxh6lq
Hyper-Sparsity in the Revised Simplex Method and How to Exploit it
2005
Computational optimization and applications
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
Each iteration of the revised simplex method requires the solution of two linear systems and a matrix vector product. ...
Analysis of the commonly-used techniques for implementing each step of the revised simplex method shows them to be inefficient when hyper-sparsity is present. ...
The authors would like to thank John Reid who brought the Gilbert-Peierls algorithm to their attention and made valuable comments on an earlier version of this paper. ...
doi:10.1007/s10589-005-4802-0
fatcat:vsma6uo4vzb4xflgrsq5kwzwqq
Leveraging Sparsity to Speed Up Polynomial Feature Expansions of CSR Matrices Using K-Simplex Numbers
[article]
2018
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Other Versions
The algorithm performs a K-degree expansion by using a bijective function involving K-simplex numbers of column indices in the original matrix to column indices in the expanded matrix. ...
This work derives the required function for the cases of K=2 and K=3 and shows its use in the K=2 algorithm. ...
Note that the point at which the sparse and dense algorithms intersect when varying d is to the right of 0.5, which is when a matrix technically becomes sparse. ...
arXiv:1803.06418v3
fatcat:arpgwegxevdu3pnhajrddrwsie
Optimization solvers: the missing link for a fully open-source energy system modelling ecosystem
2022
Zenodo
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
The proposal promotes making the world's fastest open-source solver HiGHS better and describes a plan on how to achieve this. ...
However, the developments require funds which we aim to collect with this proposal. Funds are collected over the Linux Foundation platform and can be tax-deductible. ...
One particular property of A that must be handled carefully is the existence of dense columns. ...
doi:10.5281/zenodo.6534004
fatcat:cojv53lfrncenfcmk73nrwjrj4
Fast and efficient linear programming and linear least-squares computations
1986
Computers and Mathematics with Applications
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2005; you can also visit the original URL.
The file type is application/pdf.
Pan gratefully acknowledges the support given by NSF Grants MCS 8203232 and DCR 8507573. J. Reif was supported by the Office of Naval Research, Contract No. N00014-80-C-0647. ...
On the other hand, all the estimates have been extended to the case of an arbitrary integer input matrix & in Refs [19, 20] by using some different techniques, in particular, using variable diagonals ...
This stabilization can be combined with the customary techniques of threshold pivoting, used in sparse matrix computations at the stage of determining the elimination ordering [15] (see also Remark 3 ...
doi:10.1016/0898-1221(86)90006-4
fatcat:lhm2zra3njf4nh6m6cepifq4zq
A basis-deficiency-allowing primal phase-I algorithm using the most-obtuse-angle column rule
2006
Computers and Mathematics with Applications
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
Our computational experiments with the smallest test problems from the standard NETLIB set show that a dense projected-gradient implementation largely outperforms that of the variation of the primal simplex ...
of the primal simplex method included in the commercial code TOMLAB LPSOLVE V3.0. (~) ...
If the number of basic columns equals the number of rows of the coefficient matrix, it is a normal basis; else, it is a deficient basis. Clearly, traditional simplex variants use normal bases only. ...
doi:10.1016/j.camwa.2005.11.033
fatcat:zow6jdurxrfrxdfnhymiz5y4nu
Sparse Matrix Methods in Optimization
1984
SIAM Journal on Scientific and Statistical Computing
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2011; you can also visit the original URL.
The file type is application/pdf.
product-form update; use of the Schur complement). ...
Since significant advances continue to be made with single-system solvers, we give special attention to methods that allow such solvers to be used repeatedly on a sequence of modified systems (e.g., the ...
sparse matrix techniques. ...
doi:10.1137/0905041
fatcat:yf4a5l2t5vabzi2p3ktl73hnqi
The impact of high-performance computing in the solution of linear systems: trends and problems
2000
Journal of Computational and Applied Mathematics
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
We will concentrate on direct methods of solution and consider both the case when the coe cient matrix is dense and when it is sparse. ...
We review the in uence of the advent of high-performance computing on the solution of linear equations. ...
Acknowledgements I would like to thank my colleagues Patrick Amestoy, Jacko Koster, Xiaoye Li, John Reid, and Jennifer Scott for some helpful remarks on a draft of this paper. ...
doi:10.1016/s0377-0427(00)00401-5
fatcat:v6vcoq2a7ncjtexywdeiwjmjte
Efficient parallel linear programming
1986
Operations Research Letters
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2004; you can also visit the original URL.
The file type is application/pdf.
~ce of the Karmarkar and the simplex algorithms for dense and sparse linear programs are examined. ...
Linear programming and least squares computations ate accelerated using authors' parallel algorithms for solving linear systems. The implications on the performa,. ...
of threshold pivoting, used in sparse matrix comp-'a¢ions at the stage of determining (be elimination ordering (Pissanetsky [21] ; see also [20] on the stabilization based on variable diagonal techniques ...
doi:10.1016/0167-6377(86)90085-4
fatcat:wcs2luk5dzhwhk5rva6zphmgkm
Efficient Implementation of the Simplex Method on a CPU-GPU System
2011
2011 IEEE International Symposium on Parallel and Distributed Processing Workshops and Phd Forum
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Double precision implementation is used in order to improve the quality of solutions. Computational tests have been carried out on randomly generated instances for non-sparse LP problems. ...
The Simplex algorithm is a well known method to solve linear programming (LP) problems. In this paper, we propose a parallel implementation of the Simplex on a CPU-GPU systems via CUDA. ...
Computing the entering and leaving variables: Finding the entering or leaving variables results in finding a minimum within a set of values. This can be done on GPU via reduction techniques. ...
doi:10.1109/ipdps.2011.362
dblp:conf/ipps/LalamiBB11
fatcat:lccgbtguvnguhkghhrrpyonkey
« Previous
Showing results 1 — 15 out of 3,861 results