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A Friendly Smoothed Analysis of the Simplex Method [article]

Daniel Dadush, Sophie Huiberts
2019 arXiv   pre-print
One of the most successful frameworks for understanding the simplex method was given by Spielman and Teng (JACM '04), who developed the notion of smoothed analysis.  ...  Explaining the excellent practical performance of the simplex method for linear programming has been a major topic of research for over 50 years.  ...  The first such method, and the main one used in the context of smoothed analysis, is the parametric objective method of Gass and Saaty [GS55] , dubbed the shadow (vertex) simplex method by Borgwardt  ... 
arXiv:1711.05667v4 fatcat:6k7ww7bodbffxkhsxrrabkxz4a

A friendly smoothed analysis of the simplex method

Daniel Dadush, Sophie Huiberts
2018 Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing - STOC 2018  
One of the most successful frameworks for understanding the simplex method was given by Spielman and Teng (JACM '04), who developed the notion of smoothed analysis.  ...  Explaining the excellent practical performance of the simplex method for linear programming has been a major topic of research for over 50 years.  ...  A more general method, popular in the context of average case analysis, is the self-dual parametric simplex method of Dantzig [25] .  ... 
doi:10.1145/3188745.3188826 dblp:conf/stoc/DadushH18 fatcat:d2g3rg3zcrdlxnlkhvhbwz5svi

A Friendly Smoothed Analysis of the Simplex Method

Daniel Dadush, Sophie Huiberts
2020 SIAM journal on computing (Print)  
Spielman and Teng first solve the smoothed LP with respect to an artificial"somewhat FRIENDLY SMOOTHED ANALYSIS OF SIMPLEX METHOD STOC18-453 uniform"" right-hand side b \prime , constructed to force a  ...  FRIENDLY SMOOTHED ANALYSIS OF SIMPLEX METHOD STOC18-451 dual pivots. This procedure was in fact generalized by Lemke [66] to solve linear complementarity problems.  ...  The authors would like to thank the Simons Institute program on``Bridging Continuous and Discrete Optimization,"" where some of this work was done.  ... 
doi:10.1137/18m1197205 fatcat:gbnr52kzwnam5haonc7z7co5mi

Smoothed Analysis: Analysis of Algorithms Beyond Worst Case

Bodo Manthey, Heiko Röglin
2011 it - Information Technology  
We give a gentle, not too formal introduction to smoothed analysis by means of two examples: the k-means method for clustering and the Nemhauser/Ullmann algorithm for the knapsack problem.  ...  In order to provide a more realistic performance measure that can explain the practical performance of algorithms, smoothed analysis has been introduced.  ...  Smoothed Analysis To overcome the drawbacks of both average-case and worst-case analysis and in order to explain the speed of the simplex method, Daniel A.  ... 
doi:10.1524/itit.2011.0654 fatcat:fkiqutsij5ao7idaz6t77qepdu

AQUATICS Reconstruction Software: The Design of a Diagnostic Tool Based on Computer Vision Algorithms [chapter]

Andrea Giachetti, Gianluigi Zanetti
2004 Lecture Notes in Computer Science  
In this paper we show an example of a complex application where, following criteria of efficiency, reliability and user friendliness, several computer vision techniques have been selected and customized  ...  Computer vision methods can be applied to a variety of medical and surgical applications, and many techniques and algorithms are available that can be used to recover 3D shapes and information from images  ...  Enrico Bertolazzi and Gianmarco Manzini for providing their simplex library. Work was supported by the EUTIST-M EU funding (IST-1999-20226).  ... 
doi:10.1007/978-3-540-27816-0_5 fatcat:a773lfv6tzc4poirvux4jshtle

DOTmark – A Benchmark for Discrete Optimal Transport

Jorn Schrieber, Dominic Schuhmacher, Carsten Gottschlich
2017 IEEE Access  
Along with the DOTmark we present a survey and a performance test for a cross section of established methods ranging from more traditional algorithms, such as the transportation simplex, to recently developed  ...  Inspired by this challenge, a variety of new approaches to optimal transport has been proposed in recent years and along with these new methods comes the need for a meaningful comparison.  ...  ACKNOWLEDGMENT The authors would like to thank Björn Bähre for implementing the AHA algorithm as part of a student project.  ... 
doi:10.1109/access.2016.2639065 fatcat:q6lsqzvq35bapihuborji5a4wm

Isolation and Identification of Phosphate Solubilizing and Nitrogen-Fixing Bacteria from Lake Ol'Bolossat Sediments, Kenya

Eliud Nalianya Wafula, Sylvia Injete Murunga
2020 Modern Applied Science  
These bacteria could contribute towards sustainable agriculture with a focus on reducing excessive use of commercial fertilizers.  ...  A total of 50 bacteria were isolated, 34 were obtained from Pikovskaya’s agar medium while 16 were obtained from Norris Glucose Nitrogen free medium.  ...  and value addition of major locally available biological resources [Project number.  ... 
doi:10.5539/mas.v14n10p37 fatcat:qvdtoigh6bed3fozcxpt4e3xxq

A Study on the Baryon Acoustic Oscillation with Topological Data Analysis [article]

Kai T. Kono, Tsutomu T. Takeuchi, Suchetha Cooray, Atsushi J. Nishizawa, Koya Murakami
2020 arXiv   pre-print
In this work, we analyzed the spatial distribution of galaxies with a method from the topological data analysis (TDA), in order to detect and examine the BAO signal in the galaxy distribution.  ...  We performed this analysis on a small subsample of 2000 quasars.  ...  "New Development of the Studies on Galaxy Evolution with a Method of Data Science".  ... 
arXiv:2006.02905v1 fatcat:bzidqic4mrgphhzy3423l7xl6y

Implementation of novel methods of global and nonsmooth optimization: GANSO programming library

G. Beliakov, J. Ugon
2007 Optimization  
We discuss the implementation of a number of modern methods of global and non-smooth continuous optimization in a programming library GANSO.  ...  This article outlines the main ideas behind each method, illustrates the syntaxis and usage of the library, and reports on its interfacing with Matlab and Maple packages.  ...  Given that optimization methods based on advanced mathematical theories (such as abstract convexity, non-smooth analysis) require a significant effort to implement them, availability of user-friendly programming  ... 
doi:10.1080/02331930701617429 fatcat:dql6zmuxczfpxnfdreqj2luv4u

A hyperbolic variant of the Nelder–Mead simplex method in low dimensions

Levente Lócsi
2013 Acta Universitatis Sapientiae: Mathematica  
The Nelder-Mead simplex method is a widespread applied numerical optimization method with a vast number of practical applications, but very few mathematically proven convergence properties.  ...  We present a few basic properties of this method and we also give a Matlab implementation in 2 and 3 dimensions  ...  Thanks for the friendly atmosphere at this research group.  ... 
doi:10.2478/ausm-2014-0012 fatcat:ucnyitqpbjcqjg6ymueqhqk6pm

UDECON: deconvolution optimization software for restoring high-resolution records from pass-through paleomagnetic measurements

Chuang Xuan, Hirokuni Oda
2015 Earth, Planets and Space  
Users can also export the optimized deconvolution data to a text file for analysis in other software.  ...  After the SRM sensor response is determined and loaded to the software, optimized deconvolution can be conducted using two different approaches (i.e., "Grid search" and "Simplex method") with adjustable  ...  With a simple click in UDECON, optimized deconvolution can be searched using two different methods (i.e., "Simplex method" or "Grid search") with adjustable choices of initial values or ranges for smoothness  ... 
doi:10.1186/s40623-015-0332-x fatcat:lzlppeackvdqlequw5ldcombca

Effective preparation of non-linear material models using a programmed optimization script for a nurimerical simulation of sheet-metal processing
Učinkovita priprava nelinearnih modelov materiala s programiranim optimizacijskim zapisom za numerično simulacijo obdelave pločevine

Miroslav Urbánek, Filip Tikal
2015 Materiali in Tehnologije  
The optimization script using the simplex method was made for fitting.  ...  Progressive methods and technologies are the key to the dynamic development of the automotive and electrical-engineering industries.  ...  Acknowledgement The authors of this paper gratefully acknowledge the support from the EUREKA LF12009 project: Research and Development of a New Technology of Cold Precision Forming as a Replacement for  ... 
doi:10.17222/mit.2013.248 fatcat:r35pbvto2bhwhj5wphecxysrba

Towards Clustering-friendly Representations: Subspace Clustering via Graph Filtering [article]

Zhengrui Ma, Zhao Kang, Guangchun Luo, Ling Tian
2021 arXiv   pre-print
To recover the "clustering-friendly" representation and facilitate the subsequent clustering, we propose a graph filtering approach by which a smooth representation is achieved.  ...  Especially, its comparable performance with deep learning methods emphasizes the effectiveness of the simple graph filtering scheme for many real-world applications.  ...  A number of techniques, including kernel trick, principal component analysis, canonical correlation analysis, have been developed to map high-dimensional data to a certain representation that is suitable  ... 
arXiv:2106.09874v1 fatcat:jtvfg2uqbjayhb7uu3ugcpclhi

Page 1695 of Mathematical Reviews Vol. , Issue 95c [page]

1995 Mathematical Reviews  
Part III presents the modules for the following multidimensional problems: linear systems of equations (based on a Newton-type method), linear optimization (based on the simplex method), automatic differentiation  ...  All the algorithms treated in Parts II and III share a very user- friendly construction: First, the theoretical background of the prob- lem is discussed (description of the problem, underlying mathemat  ... 

A Dual Approach for Optimal Algorithms in Distributed Optimization over Networks [article]

César A. Uribe and Soomin Lee and Alexander Gasnikov and Angelia Nedić
2020 arXiv   pre-print
Then, we study distributed optimization algorithms for non-dual friendly functions, as well as a method to improve the dependency on the parameters of the functions involved.  ...  Numerical analysis of the proposed algorithms is also provided.  ...  Uribe is supported by the National Science Foundation under grant no. CPS 15-44953. The work of A. Gasnikov was supported by RFBR 18-29-03071 mk. The work of C.A.Uribe, S. Lee, and A.  ... 
arXiv:1809.00710v3 fatcat:kpjafs6pjrc67afhqkqw6icsvy
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