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Computational experience with a bundle approach for semidefinite cutting plane relaxations of Max-Cut and Equipartition

Ilse Fischer, Gerald Gruber, Franz Rendl, Renata Sotirov
<span title="2005-10-12">2005</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/o653fqsowvcyrhw6p4gdmpdkwm" style="color: black;">Mathematical programming</a> </i> &nbsp;
Our approach provides accurate solutions to semidefinite relaxations of the Max-Cut and the Equipartition problem, which are not achievable by direct approaches based only on interior-point methods.  ...  Semidefinite Relaxations The formulation (1) of Max-Cut gives rise to the following relaxation, which has attracted a lot of attention due to the famous approximation analysis of Goemans and Williamson  ...  Acknowledgement: We thank two anonymous referees for their constructive comments and suggestions to improve an earlier version of the paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10107-005-0661-9">doi:10.1007/s10107-005-0661-9</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2yxzp7updfgurccimeyganpmva">fatcat:2yxzp7updfgurccimeyganpmva</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20070611220456/http://www.math.uni-klu.ac.at/or/Forschung/publications/bundle.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/2e/ef/2eef5105ac57942dd00dbb2a597e0a522720c27d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10107-005-0661-9"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

BiqCrunch

Nathan Krislock, Jérôme Malick, Frédéric Roupin
<span title="2017-01-02">2017</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nbwrdehgsngz7e2t5hbiap5vgq" style="color: black;">ACM Transactions on Mathematical Software</a> </i> &nbsp;
It has been successfully tested on a variety of well-known combinatorial optimization problems, such as Max-Cut, Max-k-Cluster, and Max-Independent-Set.  ...  BiqCrunch: a semidefinite branch-and-bound method for solving binary quadratic problems.  ...  ACKNOWLEDGMENTS The authors are deeply indebted to three anonymous referees whose knowledgable comments and feedback led to major improvements to both this paper and the BiqCrunch code.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/3005345">doi:10.1145/3005345</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pbgqg24elnculiecrr2zfxzl4i">fatcat:pbgqg24elnculiecrr2zfxzl4i</a> </span>
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The RPR 2 Rounding Technique for Semidefinite Programs [chapter]

Uriel Feige, Michael Langberg
<span title="">2001</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
In many of these algorithms a semidefinite relaxation of the underlying problem is solved yielding an optimal vector configuration v 1 . . . vn.  ...  Several combinatorial optimization problems can be approximated using algorithms based on semidefinite programming.  ...  For simplicity and concreteness, we shall concentrate on variants of the Max-Cut problem.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-48224-5_18">doi:10.1007/3-540-48224-5_18</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xmmnchn2kjcm7ltgzanblosvou">fatcat:xmmnchn2kjcm7ltgzanblosvou</a> </span>
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Semidefinite relaxations for partitioning, assignment and ordering problems

F. Rendl
<span title="2012-08-11">2012</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/a7azxtgamnavvcktn5y7xrjas4" style="color: black;">4OR</a> </i> &nbsp;
Semidefinite optimization is a strong tool in the study of NP-hard combinatorial optimization problems.  ...  Contrary to linear optimization with the efficiency of the Simplex method, the algorithmic treatment of semidefinite problems is much more subtle and also practically quite expensive.  ...  Acknowledgments I thank Miguel Anjos and an anonymous referee for giving numerous suggestions to improve the presentation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10288-012-0210-3">doi:10.1007/s10288-012-0210-3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/d5d3l2ob6jdi5nuz67izh4wf7u">fatcat:d5d3l2ob6jdi5nuz67izh4wf7u</a> </span>
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Semidefinite programming based approaches to the break minimization problem

Ryuhei Miyashiro, Tomomi Matsui
<span title="">2006</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/zfqmu5yfvjbg3f4h6f7a5j3jr4" style="color: black;">Computers &amp; Operations Research</a> </i> &nbsp;
We formulate the break minimization problem as MAX RES CUT and MAX 2SAT, and apply Goemans and Williamson's approximation algorithm using semidefinite programming.  ...  This paper considers the break minimization problem in sports timetabling.  ...  For MAX RES CUT, Goemans and Williamson [4] proposed a 0.878-randomized approximation algorithm using semidefinite programming.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.cor.2004.09.030">doi:10.1016/j.cor.2004.09.030</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pk466ys27bc5fmj4nsbbokj5t4">fatcat:pk466ys27bc5fmj4nsbbokj5t4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20041209203101/http://www.ism.ac.jp:80/~tsuchiya/sympo/shukai03/shukai03-papers/miyashiro.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a3/14/a314e623a22c27317ae1f25155fc4d6dd480c442.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.cor.2004.09.030"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

MADAM: A parallel exact solver for Max-Cut based on semidefinite programming and ADMM [article]

Timotej Hrga, Janez Povh
<span title="2021-04-23">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We present MADAM, a parallel semidefinite based exact solver for Max-Cut, a problem of finding the cut with maximum weight in a given graph.  ...  The algorithm uses branch and bound paradigm that applies alternating direction method of multipliers as the bounding routine to solve the basic semidefinite relaxation strengthened by a subset of hypermetric  ...  The first author also acknowledges the financial support from the Slovenian Research Agency under the program for young researchers (MR+).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2010.07839v2">arXiv:2010.07839v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tu3jus5atfeedaodojgcoujwxi">fatcat:tu3jus5atfeedaodojgcoujwxi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210427071442/https://arxiv.org/pdf/2010.07839v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/85/f0/85f0fc287b203aa2c1c6ba5a041976773c506101.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2010.07839v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Semidefinite relaxations for partitioning, assignment and ordering problems

F. Rendl
<span title="2015-09-15">2015</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/kov3rwzipzf2dmxyohqwfpxrsm" style="color: black;">Annals of Operations Research</a> </i> &nbsp;
Semidefinite optimization is a strong tool in the study of NP-hard combinatorial optimization problems.  ...  Contrary to linear optimization with the efficiency of the Simplex method, the algorithmic treatment of semidefinite problems is much more subtle and also practically quite expensive.  ...  Acknowledgments I thank Miguel Anjos and an anonymous referee for giving numerous suggestions to improve the presentation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10479-015-2015-1">doi:10.1007/s10479-015-2015-1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/c43fqkwdtjcx5pgqzes4i4doiu">fatcat:c43fqkwdtjcx5pgqzes4i4doiu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809114511/http://www.inrialpes.fr/bipop/people/malick/Docs/12-rendl.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/31/d6/31d691985e58c970ef1b03ed22442be75c65810d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10479-015-2015-1"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

sdpt3r: Semidefinite Quadratic Linear Programming in R

Adam Rahman
<span title="">2019</span> <i title="The R Foundation"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/6gg7uwwpaffsnamwmy5ra7yz5u" style="color: black;">The R Journal</a> </i> &nbsp;
The purpose of the software is to solve semidefinite quadratic linear programming (SQLP) problems, which encompasses problems such as D-optimal experimental design, the nearest correlation matrix problem  ...  As a point of difference from the current solvers in R, sdpt3r allows for log-barrier terms in the objective function, which allows for problems such as the D-optimal design of experiments to be solved  ...  to the proper side, and returns the optimal solution using sqlp. data(Andwd) data(Apdwd) C <-0.5 out <-dwd(Apdwd,Andwd,penalty) Max-kCut Similar to the Max-Cut problem, the Max-kCut problem asks, given  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.32614/rj-2018-063">doi:10.32614/rj-2018-063</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lfar6qdhevbp3c56oyhjwps7ey">fatcat:lfar6qdhevbp3c56oyhjwps7ey</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190427134202/https://journal.r-project.org/archive/2018/RJ-2018-063/RJ-2018-063.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/68/dc/68dc45263f19edcfdb427a92493c610d81962d19.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.32614/rj-2018-063"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Page 5105 of Mathematical Reviews Vol. , Issue 99g [page]

<span title="">1999</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
A method which shares many features of interior-point methods for linear and semidefinite programming is developed for solving the max-det problem.  ...  Then a duality theory for max-det problems and connections to the semidefinite programming du- ality are described.  ... 
<span class="external-identifiers"> </span>
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A hybrid constraint programming and semidefinite programming approach for the stable set problem [article]

W.J. van Hoeve
<span title="2003-02-25">2003</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This work presents a hybrid approach to solve the maximum stable set problem, using constraint and semidefinite programming.  ...  Then the subproblems are being solved using a constraint programming solver. To strengthen the semidefinite relaxation, we propose to infer additional constraints from the discrepancy structure.  ...  Preliminaries on semidefinite programming Combinatorial optimization problems that are NP-hard are often solved with the use of a relaxation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/0302307v1">arXiv:math/0302307v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qsceyqqeeve2lpyzqkfaxdzbsq">fatcat:qsceyqqeeve2lpyzqkfaxdzbsq</a> </span>
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Computational Approaches to Max-Cut [chapter]

Laura Palagi, Veronica Piccialli, Franz Rendl, Giovanni Rinaldi, Angelika Wiegele
<span title="2011-09-26">2011</span> <i title="Springer US"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/eu7t5yl3jbh5piucndzcckjubu" style="color: black;">International Series in Operations Research and Management Science</a> </i> &nbsp;
This chapter focuses on the impact that the advances in SDP algorithms have on the computation of good/optimal solutions of the Max-Cut problem.  ...  Being Max-Cut NP-hard, the computation of good upper and lower bounds is the kernel of any algorithm for computing good/optimal solutions.  ...  Acknowledgments We thank the two anonymous referees for their careful reading of the chapter, and for their constructive remarks that greatly helped to improve its presentation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-1-4614-0769-0_28">doi:10.1007/978-1-4614-0769-0_28</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gpktavkhhbczhk73dzgf4esuvy">fatcat:gpktavkhhbczhk73dzgf4esuvy</a> </span>
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A multidimensional maximum bisection problem [article]

Zoran Maksimovic
<span title="2015-06-25">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The numerical tests, made on the randomly generated graphs, indicates that the multidimensional generalization is more difficult to solve than the original problem.  ...  This work introduces a multidimensional generalization of the maximum bisection problem. A mixed integer linear programming formulation is proposed with the proof of its correctness.  ...  The expensive part of their bounding procedure is solving the basic semidefinite programming relaxation of the Max-Cut problem.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1506.07731v1">arXiv:1506.07731v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/k5yvnke7znc5fnxljjdytvnx7e">fatcat:k5yvnke7znc5fnxljjdytvnx7e</a> </span>
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A Hybrid Constraint Programming and Semidefinite Programming Approach for the Stable Set Problem [chapter]

Willem Jan van Hoeve
<span title="">2003</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
This work presents a hybrid approach to solve the maximum stable set problem, using constraint and semidefinite programming.  ...  Then the subproblems are being solved using a constraint programming solver. To strengthen the semidefinite relaxation, we propose to infer additional constraints from the discrepancy structure.  ...  Motivation Combinatorial optimization problems that are NP-hard are often solved with the use of a polynomially solvable relaxation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-45193-8_28">doi:10.1007/978-3-540-45193-8_28</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yhpdj4gc4nflxbxqd5sltf2isi">fatcat:yhpdj4gc4nflxbxqd5sltf2isi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170921195744/http://repository.cmu.edu/cgi/viewcontent.cgi?article=1536&amp;context=tepper" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/93/5d/935d876e87aa259b80809bf0c4f04ada05563a42.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-45193-8_28"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

EXPEDIS: An Exact Penalty Method over Discrete Sets [article]

Nicolo Gusmeroli, Angelika Wiegele
<span title="2021-01-03">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We introduce the exact solution method called EXPEDIS where the constrained problem is transformed into a max-cut instance, and then thewhole machinery available for max-cut can be used to solve the transformed  ...  In order to compute the maximum cut we use the solver BiqMac. Numerical results show that this algorithm can be successfully applied on various classes of problems.  ...  The authors would like to thank Sam Burer for discussions and suggestions that improved the results significantly. The authors also thank two anonymous referees for their valuable comments.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1912.09739v4">arXiv:1912.09739v4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xeepktfeejhite4nuv3j22erdq">fatcat:xeepktfeejhite4nuv3j22erdq</a> </span>
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A max-cut formulation of 0/1 programs [article]

Jean-Bernard Lasserre
<span title="2015-12-22">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We show that the linear or quadratic 0/1 programP: { c^Tx+x^TFx : A x =b; x∈{0,1}^n},can be formulated as a MAX-CUT problem whose associated graph is simply related to the matrices and ^T.Hence the whole  ...  arsenal of approximation techniques for MAX-CUT can be applied.  ...  This research was supported by a grant from the MONGE program of the Féderation Mathématique Jacques Hadamard (FMJH, Paris) and  ... 
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