Benchmarking interior point Lp/Qp solvers

IF 1.4 3区数学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Optimization Methods & Software Pub Date : 1999-01-01 DOI:10.1080/10556789908805767

H. Mittelmann

引用次数: 20

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.

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对内点Lp/Qp求解器进行基准测试

本文对BPMPD、HOPDM、LOQO、LIPSOL和SOPLEX五种LP编码进行了比较，并比较了前三种作为QP解算器的结果。由于LOQO可以解决一般的NLP问题，因此它属于另一类。对于LP/QP问题，它被证明是鲁棒的，但由于其有限的求解特性，它解决某些LP问题的速度有些慢。SOPLEX作为唯一基于simplex的程序，在一般情况下具有很强的竞争力，但在某些问题上却被最好的IPM代码所击败。在IPM代码中，BPMPD脱颖而出，而HOPDM在LP/QP问题的解决方面还没有那么完善，而是在其他环境中使用，需要其开创性的热启动功能，现在也可用于BPMPD。LIPSOL是Matlab中唯一一个优点和缺点并存的代码。它是一个纯LP求解器，因此与其他代码相比适用性有限，但它以接近BPMPD和HOPDM的效率解决LP问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Optimization Methods & Software 工程技术-计算机：软件工程

CiteScore

4.50

自引率

0.00%

发文量

审稿时长

7 months

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.