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The Power of the Combined Basic Linear Programming and Affine Relaxation for Promise Constraint Satisfaction Problems

Joshua Brakensiek, Venkatesan Guruswami, Marcin Wrochna, Stanislav Živný
2020 SIAM journal on computing (Print)  
In the field of constraint satisfaction problems (CSPs), promise CSPs are an exciting new direction of study.  ...  In a promise CSP, each constraint comes in two forms:"strict"" and"weak,"" and in the associated decision problem one must distinguish between being able to satisfy all the strict constraints versus not  ...  We thank Libor Barto, Andrei Krokhin, and Jakub Opr\v sal for useful comments and encouragement. We also thank anonymous reviewers for many helpful comments.  ... 
doi:10.1137/20m1312745 fatcat:hd7moxv3crbkbeulczbttxv7am

The Power of the Combined Basic LP and Affine Relaxation for Promise CSPs [article]

Joshua Brakensiek, Venkatesan Guruswami, Marcin Wrochna, Stanislav Živný
2020 arXiv   pre-print
In the field of constraint satisfaction problems (CSP), promise CSPs are an exciting new direction of study.  ...  In a promise CSP, each constraint comes in two forms: "strict" and "weak," and in the associated decision problem one must distinguish between being able to satisfy all the strict constraints versus not  ...  A From Relaxations to Minion Homomorphisms In this appendix, we recall the definition of the minion Q conv and prove Lemma 7 from Section 5.  ... 
arXiv:1907.04383v3 fatcat:uw43kazqtrcnlnsobu5cg4gvty

The combined basic LP and affine IP relaxation for promise VCSPs on infinite domains [article]

Caterina Viola, Stanislav Zivny
2021 arXiv   pre-print
In this work, we extend an existing tractability result to the three generalisations of CSPs combined: We give a sufficient condition for the combined basic linear programming and affine integer programming  ...  Convex relaxations have been instrumental in solvability of constraint satisfaction problems (CSPs), as well as in the three different generalisations of CSPs: valued CSPs, infinite-domain CSPs, and most  ...  We focus on the combined basic linear programming (BLP) and affine integer programming (AIP) relaxation introduced by Brakensiek and Guruswami [19] .  ... 
arXiv:2007.01779v2 fatcat:jiweubnh35clngysvhyi3azjhu

An Algorithmic Blend of LPs and Ring Equations for Promise CSPs [article]

Joshua Brakensiek, Venkatesan Guruswami
2018 arXiv   pre-print
Promise CSPs are a relaxation of constraint satisfaction problems where the goal is to find an assignment satisfying a relaxed version of the constraints.  ...  Our algorithm is based on a novel combination of linear programming and solving linear systems over rings.  ...  The authors also thank Libor Barto, Andrei Krokhin and Jakub Opršal for a myriad of helpful comments on this paper at Dagstuhl Seminar 18231 on "The Constraint Satisfaction Problem: Complexity and Approximability  ... 
arXiv:1807.05194v1 fatcat:wptigingdref3kv6oasx5xtmce

Interval optimal power flow applied to distribution networks under uncertainty of loads and renewable resources

Pengwei CHEN, Xiangning XIAO, Xuhui WANG
2018 Journal of Modern Power Systems and Clean Energy  
To satisfy constraints fully and achieve strict operational bounds under the uncertainties from loads and sources, this paper derives an interval optimal power flow (I-OPF) method employing affine arithmetic  ...  An enhanced I-OPF method based on successive linear approximation and second-order cone programming is developed to improve solution accuracy.  ...  , and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.  ... 
doi:10.1007/s40565-018-0462-9 fatcat:ljtiyijhd5bunhls2rgl26yqh4

Logic-Based Solution Methods for Optimal Control of Hybrid Systems

A. Bemporad, N. Giorgetti
2006 IEEE Transactions on Automatic Control  
In this paper, we attempt to overcome such a difficulty by combining numerical techniques for solving convex programming problems with symbolic techniques for solving constraint satisfaction problems (  ...  Current approaches are based on mixed-integer linear (or quadratic) programming (MIP), which provides the solution after solving a sequence of relaxed linear (or quadratic) programs.  ...  The basic ingredients for an integrated approach of MIP and CLP are 1) a linear program (LP) obtained by relaxing a mixed integer linear programming (MILP) problem and 2) a CLP feasibility problem.  ... 
doi:10.1109/tac.2006.876949 fatcat:5s63fkonfncizlvmylystmrx5e

Combining (Integer) Linear Programming Techniques and Metaheuristics for Combinatorial Optimization [chapter]

Günther R. Raidl, Jakob Puchinger
2008 Studies in Computational Intelligence  
After giving a brief introduction to the basics of integer linear programming, this chapter surveys existing techniques for such combinations and classifies them into ten methodological categories.  ...  Mathematical programming techniques, including (integer) linear programming based methods, and metaheuristic approaches are two highly successful streams for combinatorial problems.  ...  Acknowledgements This work is partly supported by the European RTN ADONET under grant 504438 and the "Hochschuljubiläumsstiftung" of Vienna, Austria, under contract number H-759/2005.  ... 
doi:10.1007/978-3-540-78295-7_2 fatcat:lenuq54xgzfktottkd6odh22qy

Chapter 4 Constraint Programming [chapter]

Francesca Rossi, Peter van Beek, Toby Walsh
2008 Foundations of Artificial Intelligence  
The basic idea in constraint programming is that the user states the constraints and a general purpose constraint solver is used to solve them.  ...  Constraint programming is a powerful paradigm for solving combinatorial search problems that draws on a wide range of techniques from artificial intelligence, operations research, algorithms, graph theory  ...  One of the most popular approaches to bring linear programming into CP is to create a relaxation of (some parts of) the CP problem that is linear.  ... 
doi:10.1016/s1574-6526(07)03004-0 fatcat:vrrxlx2nhjaajj27uvoepcefqa

Constraint aggregation for rigorous global optimization

Ferenc Domes, Arnold Neumaier
2014 Mathematical programming  
Using the optimality conditions, two-sided linear relaxations, the Gauss-Jordan algorithm and a directed modified Cholesky factorization, the information in the redundant constraint is turned into powerful  ...  Constraint aggregation is especially useful since it also works in a tiny neighborhood of the global optimizer, thereby reducing the cluster effect.  ...  Numerous suggestions by the referees, which markedly improved the presentation of the paper, are gratefully acknowledged.  ... 
doi:10.1007/s10107-014-0851-4 fatcat:bqofcy2wuzb7pjkc6nrvwsmak4

On the Power of Symmetric LP and SDP Relaxations

James R. Lee, Prasad Raghavendra, David Steurer, Ning Tan
2014 2014 IEEE 29th Conference on Computational Complexity (CCC)  
We study the computational power of general symmetric relaxations for combinatorial optimization problems, both in the linear programming (LP) and semidefinite programming (SDP) case.  ...  This result gives the first lower bounds for symmetric SDP relaxations of Max CSPs, and indicates that the sum-of-squares method provides the "right" SDP relaxation for this class of problems.  ...  Prasad Raghavendra and Ning Tan acknowledge support from an NSF Career Award and an Alfred P. Sloan Research Fellowship. David Steurer's research is supported by an NSF Career Award and an Alfred P.  ... 
doi:10.1109/ccc.2014.10 dblp:conf/coco/LeeRST14 fatcat:rljvsqsehvfmvnnjoz6wrtidhq

Variational Bayes in Private Settings (VIPS) (Extended Abstract)

James R. Foulds, Mijung Park, Kamalika Chaudhuri, Max Welling
2020 Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence  
We overcome this by combining: (1) an improved composition method, called the moments accountant, and (2) the privacy amplification effect of subsampling mini-batches from large-scale data in stochastic  ...  In the full paper we extend our method to a broad class of models, including Bayesian logistic regression and sigmoid belief networks.  ...  Fusing traditional solvers and learning based methods seems an promising way to bridge complex real world to the highly-abstracted CO problems, and to combine the best of the two areas.  ... 
doi:10.24963/ijcai.2020/694 dblp:conf/ijcai/YanYH20 fatcat:pc4nelo7gzfmvmsiym3ohwspxa

Advanced optimization methods for power systems

P. Panciatici, M.C. Campi, S. Garatti, S.H. Low, D.K. Molzahn, A.X. Sun, L. Wehenkel
2014 2014 Power Systems Computation Conference  
The practical relevance of these developments for power systems planning and operation are discussed, and the opportunities for combining them, together with high-performance computing and big data infrastructures  ...  In practice, these problems are generally large-scale, non-linear, subject to uncertainties, and combine both continuous and discrete variables.  ...  The work of S. H. Low is supported by NSF, DoE, and SCE. The work of D.K. Molzahn is supported by the Dow Sustainability Fellowship at the University of Michigan. The work of L.  ... 
doi:10.1109/pscc.2014.7038504 dblp:conf/pscc/PanciaticiCGLMS14 fatcat:w6lh2n4cpvhl5fbcomdmnwvwye

Complete search in continuous global optimization and constraint satisfaction

Arnold Neumaier
2004 Acta Numerica  
This survey covers the state of the art of techniques for solving generalpurpose constrained global optimization problems and continuous constraint satisfaction problems, with emphasis on complete techniques  ...  Then a discussion of important problem transformations follows, in particular of linear, convex, and semilinear (= mixed integer linear) relaxations that are important for handling larger problems.  ...  I also want to thank Hermann Schichl for many discussions and for comments on earlier versions of this survey, and Christian Jansson and Nick Sahinidis for additional comments that improved the paper.  ... 
doi:10.1017/s0962492904000194 fatcat:phckdsbkevdahcawdroqwwgoeq

Algebraic Theory of Promise Constraint Satisfaction Problems, First Steps [chapter]

Libor Barto
2019 Lecture Notes in Computer Science  
This paper explains an extension of this theory to a much broader class of computational problems, the promise CSPs, which includes relaxed versions of CSPs such as the problem of finding a 137-coloring  ...  This fundamental question now has a satisfactory answer for a quite broad class of computational problems, so called fixed-template constraint satisfaction problems (CSPs) -- it has turned out that their  ...  This idea proved greatly useful for an interesting class of problems, so called fixed-template constraint satisfaction problems (CSPs), and eventually led to a full complexity classification result [17  ... 
doi:10.1007/978-3-030-25027-0_1 fatcat:yqtjs3izxzcy3atal3l4w7ienq

Optimal power flow: a bibliographic survey II

Stephen Frank, Ingrida Steponavice, Steffen Rebennack
2012 Energy Systems, Springer Verlag  
Over the past half-century, Optimal Power Flow (OPF) has become one of the most important and widely studied nonlinear optimization problems.  ...  In general, OPF seeks to optimize the operation of electric power generation, transmission, and distribution networks subject to system constraints and control limits.  ...  Each of the objectives and constraints are expressed as a fuzzy set, where a satisfaction parameter is assigned.  ... 
doi:10.1007/s12667-012-0057-x fatcat:sysa5sl3j5ez3au4yqipyrvfuy
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