{"title":"对内点Lp/Qp求解器进行基准测试","authors":"H. Mittelmann","doi":"10.1080/10556789908805767","DOIUrl":null,"url":null,"abstract":"In this work results of a comparison of five LP codes, BPMPD, HOPDM, LOQO, LIPSOL, and SOPLEX are reported and also of the first three as QP solvers. Since LOQO can solve general NLP problems it is in another class. For LP/QP problems it proves to be robust but it solves certain LP problems somewhat slower due to its limited presolve feature. SOPLEX as the only simplex-based program is highly competitive in general but is beaten by the best IPM codes on certain problems. Among the IPM codes BPMPD stands out while HOPDM has not been perfected as much for the solution of LP/QP problems but rather for use in other contexts requiring its pioneering warmstart feature which is now also available for BPMPD. LIPSOL is the only code in Matlab which has both advantages and disadvantages. It is a pure LP solver and has thus limited applicability compared to the other codes but solves LP problems with an efficiency close to that of BPMPD and HOPDM.","PeriodicalId":54673,"journal":{"name":"Optimization Methods & Software","volume":"72 1","pages":"655-670"},"PeriodicalIF":1.4000,"publicationDate":"1999-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"20","resultStr":"{\"title\":\"Benchmarking interior point Lp/Qp solvers\",\"authors\":\"H. Mittelmann\",\"doi\":\"10.1080/10556789908805767\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this work results of a comparison of five LP codes, BPMPD, HOPDM, LOQO, LIPSOL, and SOPLEX are reported and also of the first three as QP solvers. Since LOQO can solve general NLP problems it is in another class. For LP/QP problems it proves to be robust but it solves certain LP problems somewhat slower due to its limited presolve feature. SOPLEX as the only simplex-based program is highly competitive in general but is beaten by the best IPM codes on certain problems. Among the IPM codes BPMPD stands out while HOPDM has not been perfected as much for the solution of LP/QP problems but rather for use in other contexts requiring its pioneering warmstart feature which is now also available for BPMPD. LIPSOL is the only code in Matlab which has both advantages and disadvantages. It is a pure LP solver and has thus limited applicability compared to the other codes but solves LP problems with an efficiency close to that of BPMPD and HOPDM.\",\"PeriodicalId\":54673,\"journal\":{\"name\":\"Optimization Methods & Software\",\"volume\":\"72 1\",\"pages\":\"655-670\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"1999-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"20\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Optimization Methods & Software\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1080/10556789908805767\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, SOFTWARE ENGINEERING\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Optimization Methods & Software","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1080/10556789908805767","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, SOFTWARE ENGINEERING","Score":null,"Total":0}
In this work results of a comparison of five LP codes, BPMPD, HOPDM, LOQO, LIPSOL, and SOPLEX are reported and also of the first three as QP solvers. Since LOQO can solve general NLP problems it is in another class. For LP/QP problems it proves to be robust but it solves certain LP problems somewhat slower due to its limited presolve feature. SOPLEX as the only simplex-based program is highly competitive in general but is beaten by the best IPM codes on certain problems. Among the IPM codes BPMPD stands out while HOPDM has not been perfected as much for the solution of LP/QP problems but rather for use in other contexts requiring its pioneering warmstart feature which is now also available for BPMPD. LIPSOL is the only code in Matlab which has both advantages and disadvantages. It is a pure LP solver and has thus limited applicability compared to the other codes but solves LP problems with an efficiency close to that of BPMPD and HOPDM.
期刊介绍：
Optimization Methods and Software
publishes refereed papers on the latest developments in the theory and realization of optimization methods, with particular emphasis on the interface between software development and algorithm design.
Topics include:
Theory, implementation and performance evaluation of algorithms and computer codes for linear, nonlinear, discrete, stochastic optimization and optimal control. This includes in particular conic, semi-definite, mixed integer, network, non-smooth, multi-objective and global optimization by deterministic or nondeterministic algorithms.
Algorithms and software for complementarity, variational inequalities and equilibrium problems, and also for solving inverse problems, systems of nonlinear equations and the numerical study of parameter dependent operators.
Various aspects of efficient and user-friendly implementations: e.g. automatic differentiation, massively parallel optimization, distributed computing, on-line algorithms, error sensitivity and validity analysis, problem scaling, stopping criteria and symbolic numeric interfaces.
Theoretical studies with clear potential for applications and successful applications of specially adapted optimization methods and software to fields like engineering, machine learning, data mining, economics, finance, biology, or medicine. These submissions should not consist solely of the straightforward use of standard optimization techniques.
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