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A New Practically Efficient Interior Point Method for LP

Katta Murty
2006 Algorithmic Operations Research   unpublished
Here we discuss a gravitational method of type (c) that behaves like an interior point method [8,20, 21].  ...  Key words: Linear programming (LP), Dantzig's simplex method, boundary methods, gravitational method, interior point method, avoiding zigzagging, solving LPs without matrix inversions, strongly polynomial  ...  The Gravitational Interior Point Method for LP Here we state the whole method.  ... 

Improving a primal–dual simplex-type algorithm using interior point methods

T. Glavelis, N. Ploskas, N. Samaras
2018 Optimization  
It applies an interior point method for a few iterations leading to significant improvement of the objective function value.  ...  This paper presents a hybrid algorithm that combines the strengths of interior point methods and exterior point simplex algorithms.  ...  In 1984, a totally new method arose and changed everything in LP [17] ; Interior Point Methods (IPMs) revealed that the simplex algorithm was not the only way for solving an optimization problem.  ... 
doi:10.1080/02331934.2018.1523906 fatcat:jldy326e3jayzn2sa5mz2ugo7y

An extension of an interior-point method for entropy minimization

I.F. Gorodnitsky
1999 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258)  
The paper presents a novel algorithm for entropy optimization. The algorithm is motivated by the efficient interior-point methods developed in Linear Programming.  ...  I show that for some entropy functions the proposed algorithm has superior convergence properties when compared to comparable the interior-point methods.  ...  Interior-point Methods The notation used here and throughout the rest of the paper follows closely the notation in [7] . Interior-point methods were first developed to efficiently solve LP problems.  ... 
doi:10.1109/icassp.1999.756320 dblp:conf/icassp/Gorodnitsky99 fatcat:zovzzmh25bc4xn7ey3bcpnu66e

Conic Sampling: An Efficient Method for Solving Linear and Quadratic Programming by Randomly Linking Constraints within the Interior

Oliver Serang, Jérémie Bourdon
2012 PLoS ONE  
Existing approaches to LP have been dominated by a small group of methods, and randomized algorithms have not enjoyed popularity in practice.  ...  This paper introduces a novel randomized method of solving LP problems by moving along the facets and within the interior of the polytope along rays randomly sampled from the polyhedral cones defined by  ...  Acknowledgments I am grateful for the contributions of Jeff Bilmes and William Noble, without whom this work would not have been possible.  ... 
doi:10.1371/journal.pone.0043706 pmid:22952741 pmcid:PMC3428371 fatcat:cpm3sp4iibaathvchzlfju2bzu

Introducing Interior-Point Methods for Introductory Operations Research Courses and/or Linear Programming Courses

Goran Lesaja
2009 Open Operational Research Journal  
In recent years the introduction and development of Interior-Point Methods has had a profound impact on optimization theory as well as practice, influencing the field of Operations Research and related  ...  Development of these methods has quickly led to the design of new and efficient optimization codes particularly for Linear Programming.  ...  For a while, Kranich [15] maintained a detailed bibliography on interior-point methods. For a number of years, S.  ... 
doi:10.2174/1874243200903010001 fatcat:qbdkad3c7bepvijs6m7zjhvgvy

The design and application of IPMLO. A FORTRAN library for linear optimization with interior point methods

J. Gondzio, D. Tachat
1994 Reserche operationelle  
The authors are grateful to anonymous référée for careful reading of the manuscript and pointing out a number of improvements.  ...  AVAILABILITY OF CODE It is our intention to make the IPMLO code available for any research purposes. More information regarding this can be obtained by contacting Jacek Gondzio.  ...  Comparison of IPMLO with this benchmark LP code does not aim to draw gênerai conclusions on the performance of two practicable LP approaches: interior point and simplex ones.  ... 
doi:10.1051/ro/1994280100371 fatcat:6fjzzwk54rht3eu7dvbstgeakm

An Improved Affine-Scaling Interior Point Algorithm

Douglas Kwasi Boah, Stephen Boakye Twum
2019 Journal of Applied Mathematics and Physics  
The algorithm can be very useful for development of faster software packages for solving linear programming problems using the interior-point methods.  ...  In this paper, an Improved Affine-Scaling Interior Point Algorithm for Linear Programming has been proposed.  ...  Introduction The Simplex Method (SM) remained a popular solution method of practical linear programming (LP) problems, until the development of interior point methods.  ... 
doi:10.4236/jamp.2019.710172 fatcat:hg2bvl5rdnehxfuow7mxyvoani

Interior-Point Algorithms for Linear-Programming Decoding [article]

Pascal O. Vontobel
2008 arXiv   pre-print
Interior-point algorithms constitute a very interesting class of algorithms for solving linear-programming problems.  ...  In this paper we study efficient implementations of such algorithms for solving the linear program that appears in the linear-programming decoder formulation.  ...  This results in a new current point.  ... 
arXiv:0802.1369v1 fatcat:7kcf7naq6jfrtgaha4nwzusajm

Interior-point algorithms for linear-programming decoding

Pascal O. Vontobel
2008 2008 Information Theory and Applications Workshop  
Interior-point algorithms constitute a very interesting class of algorithms for solving linear-programming problems.  ...  In this paper we study efficient implementations of such algorithms for solving the linear program that appears in the linearprogramming decoder formulation.  ...  This results in a new current point.  ... 
doi:10.1109/ita.2008.4601085 fatcat:5p72x7hvwngs3c23hgfdujcjga

Developments in linear and integer programming

K Darby-Dowman, J M Wilson
2002 Journal of the Operational Research Society  
A computational view of interior point methods. In: Beasley J E (ed) Advances in Linear and Integer Programming, Oxford University Press: Oxford, pp 103 -144.  ...  A new polynomial-time algorithm for linear programming. Combinatorica 4: 373-395. 13. Goldfarb D and Reid J K (1977). A practicable steepest-edge simplex algorithm.  ...  and Bland 25 researchers have developed new methods for selecting pivots in LP solution algorithms.  ... 
doi:10.1057/palgrave.jors.2601435 fatcat:ea4t3ak2mbhldldng3cah2sxbe

Page 8245 of Mathematical Reviews Vol. , Issue 98M [page]

1998 Mathematical Reviews  
Chapter 4 contains a discussion of interior point methods and a description of Dikin’s primal affine scaling method. Chapter 5 covers duality in LP.  ...  The performance of the INFCP algorithm is compared to those of practical interior- point algorithms.  ... 

Solving a class of LP problems with a primal-dual logarithmic barrier method

Jacek Gondzio, Marek Makowski
1995 European Journal of Operational Research  
Such optimization problems are often large LP problems and therefore the solver should be both efficient, robust and royalty free for distribution.  ...  The primary motivation for this research was to provide an efficient and distributable solver for optimization problems frequently generated in collaborative studies of the Food and Agriculture Project  ...  First, to apply the HOPDM (higher order primal-dual method cf [I, 2] ), which is an efficient implementation of the primal-dual interior point method, for solving large real-life linear programming (LP  ... 
doi:10.1016/0377-2217(93)e0323-p fatcat:dad7xcldjzhqtdkto5zq3ohnpa

Scalable Method for Linear Optimization of Industrial Processes [article]

Leonid B. Sokolinsky, Irina M. Sokolinskaya
2020 arXiv   pre-print
In many cases, this problem can be reduced to a large-scale linear programming (LP) problem. The article is devoted to the new method for solving large-scale LP problems.  ...  This method is called the "apex-method". The apex-method uses the predictor-corrector framework. The predictor step calculates a point belonging to the feasible region of LP problem.  ...  The simplex method was found to be efficient for solving a large class of LP problems.  ... 
arXiv:2006.14921v1 fatcat:bqjpn542hjabjnv6nltshozequ

Solving large-scale optimization problems related to Bell's Theorem

Jacek Gondzio, Jacek A. Gruca, J.A. Julian Hall, Wiesław Laskowski, Marek Żukowski
2014 Journal of Computational and Applied Mathematics  
interior point method.  ...  The article compares the performances of the existing implementation of the method, where the LPs are solved with the simplex method, and our new implementation, where the LPs are solved with a matrix-free  ...  Wies law Laskowski and MarekŻukowski are supported by a MNiSW Grant IdP2011 00361 (Ideas Plus).  ... 
doi:10.1016/ fatcat:xkvpkhxuznaalgpjng3e5wol5m

Page 5018 of Mathematical Reviews Vol. , Issue 95h [page]

1995 Mathematical Reviews  
Some basic concepts of interior point methods (IPMs) for linear programming are reconsidered in this paper. Practically all IPMs use some weighting and scaling.  ...  The corrector step uses a procedure employed in a feasible-interior-point algorithm.  ... 
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