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A Scalable Semidefinite Relaxation Approach to Grid Scheduling [article]

Ramtin Madani, Alper Atamturk, Ali Davoudi
<span title="2017-07-12">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We design a polynomial-time solvable third-order semidefinite programming (TSDP) relaxation, with the aim of finding a near globally optimal solution for the original NP-hard problem.  ...  In this paper, we propose for the first time a computational method, which is capable of solving large-scale power system scheduling problems with thousands of generating units, while accurately incorporating  ...  A. Atamtürk is supported, in part, by grant FA9550-10-1-0168 from the Office of the Assistant Secretary of Defense for Research and Engineering.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1707.03541v1">arXiv:1707.03541v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/oivbx4ragvc6pgrps2dlyqbfry">fatcat:oivbx4ragvc6pgrps2dlyqbfry</a> </span>
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Simple proof of the impossibility of bit commitment in generalized probabilistic theories using cone programming

Jamie Sikora, John Selby
<span title="2018-04-03">2018</span> <i title="American Physical Society (APS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/z3u6fzrh4fdvhnzujueyvzipwi" style="color: black;">Physical Review A</a> </i> &nbsp;
Our proof relies crucially on a formulation of cheating strategies as cone programs, a natural generalisation of semidefinite programs.  ...  Bit-commitment is a fundamental cryptographic task, in which Alice commits a bit to Bob such that she cannot later change the value of the bit, while, simultaneously, the bit is hidden from Bob.  ...  When K is the cone of positive semidefinite matrices we recover semidefinite programming and when K is the nonnegative orthant, we recover linear programming.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreva.97.042302">doi:10.1103/physreva.97.042302</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5q7ajubyofecbnznoxetix2hgy">fatcat:5q7ajubyofecbnznoxetix2hgy</a> </span>
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A Mixed-Integer SDP Solution Approach to Distributionally Robust Unit Commitment with Second Order Moment Constraints [article]

Xiaodong Zheng, Haoyong Chen, Yan Xu, Zhengmao Li, Zhenjia Lin, Zipeng Liang
<span title="2019-10-27">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Based on the verification of strong duality of the semidefinite programming (SDP) problems, we propose a cutting plane algorithm for solving the MI-SDPs; we also introduce a SDP relaxation for the feasibility  ...  The resulting problem is a two-stage distributionally robust unit commitment with second order moment constraints, and we show that it can be recast as a mixed-integer semidefinite programming (MI-SDP)  ...  As a result, the solution may commit redundant units and enforce too much reserve.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1910.12187v1">arXiv:1910.12187v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dothiwxjlfcori3jwwdkzzi66q">fatcat:dothiwxjlfcori3jwwdkzzi66q</a> </span>
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Convex power flow models for scalable electricity market modelling

Frederik Geth, Reinhilde D'Hust, Dirk Van Hertem
<span title="2018-06-12">2018</span> <i title="Zenodo"> Zenodo </i> &nbsp;
The hierarchy of the approaches is detailed, as well as the loss of properties resulting from the relaxation process.  ...  Optimal power flow problems and market clearing approaches are converging: cost-optimal scheduling of loads and generators should be performed while taking the grid's physics and operational envelopes  ...  ACKNOWLEDGMENTS The research leading to these results has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 691405.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5281/zenodo.1321189">doi:10.5281/zenodo.1321189</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/a4nwvo2gmbbsrdyagss22qvaje">fatcat:a4nwvo2gmbbsrdyagss22qvaje</a> </span>
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Preface

Dimitri P. Bertsekas, Zhi-Quan Luo
<span title="2011-06-04">2011</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/o653fqsowvcyrhw6p4gdmpdkwm" style="color: black;">Mathematical programming</a> </i> &nbsp;
The paper by Zheng et al. deals with semidefinite relaxation of nonconvex quadratically constrained quadratic programming.  ...  He coauthored with his advisor Dimitri Bertsekas, a series of papers on relaxation methods and monotropic programming, as well as a publicly available network optimization program, called RELAX, which  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10107-011-0473-z">doi:10.1007/s10107-011-0473-z</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rpnymm26tzg2bkinhq663tlrkm">fatcat:rpnymm26tzg2bkinhq663tlrkm</a> </span>
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Benders' decomposition of the unit commitment problem with semidefinite relaxation of AC power flow constraints [article]

M. Paredes, L. S. A. Martins, S. Soares, Hongxing Ye
<span title="2019-03-06">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper we present a formulation of the unit commitment problem with AC power flow constraints.  ...  It is solved by a Benders decomposition in which the unit commitment master problem is formulated as a mixed-integer problem with linearization of the power generation constraints for improved convergence  ...  The authors would like to thank Professor Mohammad Shahidehpour of Illinois Institute of Technology for his invaluable insights in the early versions of this manuscript.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1903.02628v1">arXiv:1903.02628v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/l24jw3jspfchzpyugmij5wbc3i">fatcat:l24jw3jspfchzpyugmij5wbc3i</a> </span>
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On Valid Inequalities for Quadratic Programming with Continuous Variables and Binary Indicators [chapter]

Hongbo Dong, Jeff Linderoth
<span title="">2013</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;
Second, we show that all perspective constraints are a special case of lifted-concave-QPB inequalities, and we further show that adding the perspective constraints to a semidefinite programming relaxation  ...  This structure appears when deriving strong relaxations for mixed integer quadratic programs (MIQPs).  ...  lifted-concave-QPB inequalities can be accomplished by solving a semidefinite programming problem of size polynomial in n.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-36694-9_15">doi:10.1007/978-3-642-36694-9_15</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2nhrrm4l5fgj7ik6s4dkouzsiy">fatcat:2nhrrm4l5fgj7ik6s4dkouzsiy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170128002511/http://www.mcs.anl.gov/MACS/files/2013/08/On-Valid-Inequalities-for-Quadradic-Prog.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/b3/f0/b3f01315c1026525343d1639ac1d6a8e5de2a0a9.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-36694-9_15"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Recent Advances in Mathematical Programming with Semi-continuous Variables and Cardinality Constraint

Xiaoling Sun, Xiaojin Zheng, Duan Li
<span title="">2013</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5s6d4kiydrdtvfcj4s3umgjnky" style="color: black;">Journal of the Operations Research Society of China</a> </i> &nbsp;
This class of problems can be modeled as mixed-integer programs with special structures and are in general NP-hard.  ...  We survey in this paper these recent developments for this challenging class of mathematical programming problems.  ...  and unit commitment problem in power system.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s40305-013-0004-0">doi:10.1007/s40305-013-0004-0</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/i43f223gwbcarnenh5xes7bipe">fatcat:i43f223gwbcarnenh5xes7bipe</a> </span>
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Global Solution Strategies for the Network-Constrained Unit Commitment Problem With AC Transmission Constraints

Jianfeng Liu, Carl D. Laird, Joseph K. Scott, Jean-Paul Watson, Anya Castillo
<span title="">2019</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/gnhkf3aieraxhlw7vpy6whnksy" style="color: black;">IEEE Transactions on Power Systems</a> </i> &nbsp;
We propose a novel global solution algorithm for the network-constrained unit commitment problem incorporating a nonlinear alternating current model of the transmission network, which is a nonconvex mixed-integer  ...  We exploit the mathematical structure of the unit commitment problem with AC power flow constraints (UC-AC) and leverage optimization-based bounds tightening, second-order cone relaxations, and piecewise  ...  In our approach, convex relaxations of the nonlinear AC transmission constraints play a crucial role, as strong relaxations can improve the tightness of the mixed-ifnteger lowerbounding problem, leading  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tpwrs.2018.2876127">doi:10.1109/tpwrs.2018.2876127</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rvmq53chmnbvveaqcp3kegqg3q">fatcat:rvmq53chmnbvveaqcp3kegqg3q</a> </span>
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A copositive approach for two-stage adjustable robust optimization with uncertain right-hand sides

Guanglin Xu, Samuel Burer
<span title="2017-12-27">2017</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jkj6zja2ubhybmybu4bm5sgkwe" style="color: black;">Computational optimization and applications</a> </i> &nbsp;
We prove that under standard and simple conditions, the two-stage problem can be reformulated as a copositive optimization problem, which in turn leads to a class of tractable, semidefinite-based approximations  ...  ARO can be significantly less conservative than regular robust optimization, and real-world applications of ARO abound: unit commitment in renewable energy B Guanglin Xu where y(u) is a vector variable  ...  discussions, for relaying the specific parameters of the instance presented in Sect. 5.2, and for pointing out an error in one of our codes.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10589-017-9974-x">doi:10.1007/s10589-017-9974-x</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kjvnr3r2kve3neqx3c2l445tou">fatcat:kjvnr3r2kve3neqx3c2l445tou</a> </span>
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A Review on Unit Commitment Algorithms for the Italian Electricity Market

Maria Carmen Falvo, Stefano Panella, Mauro Caprabianca, Federico Quaglia
<span title="2021-12-21">2021</span> <i title="MDPI AG"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/a2yvk5xhdnhpxjnk6yd33uudqq" style="color: black;">Energies</a> </i> &nbsp;
This paper focuses on the state-of-the-art of unit commitment (UC) and economic dispatch (ED) algorithms suitable for the Italian electricity market.  ...  In view of the spread of renewable energy systems (RES), the desired UC algorithm should be able to properly consider the uncertainty affecting key input variables into the formulation of the problem,  ...  Conflicts of Interest: The authors declare no conflict of interest. Energies 2022, 15, 18  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/en15010018">doi:10.3390/en15010018</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dgfm4h75uvconnv5eijfbkdyqi">fatcat:dgfm4h75uvconnv5eijfbkdyqi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220502065914/https://mdpi-res.com/d_attachment/energies/energies-15-00018/article_deploy/energies-15-00018-v2.pdf?version=1640151361" 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/3e/11/3e11c06ac84d04c689409ffa95a0fa2bd231f761.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/en15010018"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> mdpi.com </button> </a>

Essentially optimal interactive certificates in linear algebra

Jean-Guillaume Dumas, Erich Kaltofen
<span title="">2014</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p5cu7ybzmnd3jpp7pphgogfzpi" style="color: black;">Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation - ISSAC &#39;14</a> </i> &nbsp;
Our certificates can be verified in Monte-Carlo bit complexity (n 2 log A ) 1+o(1) , where log A is the bit size of the integer entries, solving an open problem in [Kaltofen, Nehring, Saunders, Proc.  ...  We give algorithms that compute essentially optimal certificates for the positive semidefiniteness, Frobenius form, characteristic and minimal polynomial of an n × n dense integer matrix A.  ...  Acknowledgments We thank Brice Boyer , Shafi Goldwasser , Clément Pernet , Jean-Louis Roch , Guy Rothblum , Justin Thaler and the referees for their helpful comments.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2608628.2608644">doi:10.1145/2608628.2608644</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/issac/DumasK14.html">dblp:conf/issac/DumasK14</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kaa52pbrwvao7itggjkhqbpof4">fatcat:kaa52pbrwvao7itggjkhqbpof4</a> </span>
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Conic Relaxations for Power System State Estimation with Line Measurements [article]

Yu Zhang, Ramtin Madani, Javad Lavaei
<span title="2017-04-01">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Motivating by these limitations, we propose a novel convexification framework for the PSSE using semidefinite programming (SDP) and second-order cone programming (SOCP) relaxations.  ...  Strong theoretical results are derived to quantify the optimal solution of the penalized SDP problem, which is shown to possess a dominant rank-one component formed by lifting the true voltage vector.  ...  The proposed convex programs are in the form of semidefinite programming (SDP), where a convex objective is designed as a surrogate of the rank-one constraint to guarantee the exactness of the SDP relaxation  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1704.00133v1">arXiv:1704.00133v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cj2vnwo4urckpd3imaunmruvia">fatcat:cj2vnwo4urckpd3imaunmruvia</a> </span>
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Conic Relaxations for Power System State Estimation With Line Measurements

Yu Zhang, Ramtin Madani, Javad Lavaei
<span title="">2018</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3rnmvpwtdjebhatxivur765gie" style="color: black;">IEEE Transactions on Control of Network Systems</a> </i> &nbsp;
Motivating by these limitations, we propose a novel convexification framework for the PSSE using semidefinite programming (SDP) and second-order cone programming (SOCP) relaxations.  ...  Strong theoretical results are derived to quantify the optimal solution of the penalized SDP problem, which is shown to possess a dominant rank-one component formed by lifting the true voltage vector.  ...  The proposed convex programs are in the form of semidefinite programming (SDP), where a convex objective is designed as a surrogate of the rank-one constraint to guarantee the exactness of the SDP relaxation  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tcns.2017.2691473">doi:10.1109/tcns.2017.2691473</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/g6cjvzr5rvad3inuj3qdx3e7ue">fatcat:g6cjvzr5rvad3inuj3qdx3e7ue</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200313100226/https://escholarship.org/content/qt4vw168fn/qt4vw168fn.pdf?t=p696j6" 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/56/42/564248259e7635116c94d5b5d5c647e4f83d3f6d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tcns.2017.2691473"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Optimal Power Flow as a Polynomial Optimization Problem

Bissan Ghaddar, Jakub Marecek, Martin Mevissen
<span title="">2016</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/gnhkf3aieraxhlw7vpy6whnksy" style="color: black;">IEEE Transactions on Power Systems</a> </i> &nbsp;
Formulating the alternating current optimal power flow (ACOPF) as a polynomial optimization problem makes it possible to solve large instances in practice and to guarantee asymptotic convergence in theory  ...  A recent line of research proposed by Bai et al. [1] applied semidefinite programming (SDP) to the OPF problem. Lavaei et al.  ...  For example, besides the minimization of power generation costs, other objectives can be formulated using PP, including minimization of power generation costs with unit commitment costs, minimization of  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tpwrs.2015.2390037">doi:10.1109/tpwrs.2015.2390037</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6g7sz5gapbd2jipllvosh4wtea">fatcat:6g7sz5gapbd2jipllvosh4wtea</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20150921222518/http://researcher.watson.ibm.com/researcher/files/ie-MARTMEVI/GMM2014.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/4e/be/4ebe5b259f52a8136fd3d8fd82d9ff7a08c01c11.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tpwrs.2015.2390037"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>
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