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	<title>丕子 &#187; QP</title>
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		<title>二次规划Quadratic Programming(QP)以及工具</title>
		<link>http://www.zhizhihu.com/html/y2009/510.html</link>
		<comments>http://www.zhizhihu.com/html/y2009/510.html#comments</comments>
		<pubDate>Fri, 16 Oct 2009 01:26:52 +0000</pubDate>
		<dc:creator>丕子</dc:creator>
				<category><![CDATA[科研]]></category>
		<category><![CDATA[QP]]></category>
		<category><![CDATA[机器学习]]></category>

		<guid isPermaLink="false">http://二次规划是非线形规划中一类特殊的数学规划问题，它的解是可以通过求解得到的。通常通过解其库恩—塔克条件（KT条件）,获取一个KT条件的解称为KT对，其中与原问题的变量对应的部分称为KT点。　　二次规划分为凸二次规划与非凸二次规划，前者的KT点便是其全局极小值点，而后者的KT点可能连局部极小值点都不是。若它的目标函数是二次函数!--more--，则约束条件是线性的。由于求解二次规划的方法很多，所以较为复杂；其较简便易行的是沃尔夫法，它是依据库恩－塔克条件，在线性规划单纯形法的基础上加以修正而成的。此外</guid>
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			<content:encoded><![CDATA[<p>二次规划是非线形规划中一类特殊的数学规划问题，它的解是可以通过求解得到的。通常通过解其库恩—塔克条件（KT条件）,获取一个KT条件的解称为KT对，其中与原问题的变量对应的部分称为KT点。<br />
　　二次规划分为凸二次规划与非凸二次规划，前者的KT点便是其全局极小值点，而后者的KT点可能连局部极小值点都不是。若它的目标函数是二次函数<span id="more-510"></span>，则约束条件是线性的。由于求解二次规划的方法很多，所以较为复杂；其较简便易行的是沃尔夫法，它是依据库恩－塔克条件，在线性规划单纯形法的基础上加以修正而成的。此外还有莱姆基法、毕尔法、凯勒法等。</p>
<ul>
<li><strong>Quadratic programming codes:</strong>
<ul>
<li><a href="http://www-unix.mcs.anl.gov/~leyffer/solvers.html">BQPD</a> from Roger Fletcher</li>
<li><a href="http://www.ilog.com/products/cplex/product/barrier.cfm">CPLEX</a> Barrier/QP solver</li>
<li><a href="http://www.ilog.com/products/cplex/product/simplex.cfm">CPLEX</a> Simplex/QP solver</li>
<li><a href="http://www.ilog.com/products/cplex/product/mip.cfm">CPLEX</a> Mixed-integer QP solver</li>
<li>The <a href="http://www.dashoptimization.com/home/products/products_optimizer.html">Xpress-MP</a> Newton-barrier QP solver from Dash Optimization</li>
<li><a href="http://www.maths.ed.ac.uk/~gondzio/software/hopdm.html">HOPDM</a> from Jacek Gondzio and Anna Altman</li>
<li><a href="http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Blurbs/lindo.html">LINDO</a></li>
<li>The packages QPC, QPB and QPA from <a href="http://galahad.rl.ac.uk/galahad-www/">GALAHAD</a></li>
<li>The packages VE02, VE09, VE17, HSL_VE12 and HSL_VE19 from <a href="http://www.cse.clrc.ac.uk/Activity/HSL">HSL</a> (formerly known as the Harwell Subroutine Library</li>
<li><a href="http://www.orfe.princeton.edu/~loqo/">LOQO</a> from Bob Vanderbei</li>
<li><a href="http://www.mat.univie.ac.at/~neum/software/minq/">MINQ</a> for convex general and non-convex bound constrained problems, in Matlab, by Arnold Neumaier</li>
<li><a href="http://www.caam.rice.edu/~zhang/circut/">CirCut</a> for finding approximate solutions to certain binary quadratic programs, including the Max-Cut and the Max-Bisection problems, by Yin Zhang</li>
<li>The subroutines E04NCF, E04NFF, E04NKF, H02CBF and H02CEF from the <a href="http://www.nag.co.uk/numeric/fl/FLdescription.asp">NAG fortran</a> library</li>
<li>The package nag_qp_sol from the <a href="http://www.nag.co.uk/numeric/fn/FNdescription.asp">NAG fl90</a> library</li>
<li>The subroutines nag_opt_lin_lsq and nag_opt_sparse_convex_qp from the <a href="http://www.nag.co.uk/numeric/cl/CLdescription.asp">NAG C</a> library</li>
<li><a href="http://ziena.com/knitro.html">KNITRO</a> from Ziena Optimization Inc. is highly QP-capable.</li>
<li><a href="http://www.sbsi-sol-optimize.com/asp/sol_product_lssol.htm">LSSOL</a> from SOL Optimization Software</li>
<li><a href="http://www.cs.wisc.edu/~swright/ooqp/">OOQP</a> by Mike Gertz and Steve Wright</li>
<li><a href="http://www.sbsi-sol-optimize.com/asp/sol_product_qpopt.htm">QPOPT</a> again from SOL Optimization Software</li>
<li>The C/Python <a href="http://abel.ee.ucla.edu/cvxopt/userguide/coneprog.html#quadratic-programming">QP</a> package which is part of <a href="http://abel.ee.ucla.edu/cvxopt/">CVXOPT</a></li>
<li>The package <a href="http://www-out.bell-labs.com/project/IQP/">IQP</a>, by Linda Kaufman and Jessica Hodgins, from the <a href="http://www.bell-labs.com/project/PORT/">PORT</a> Mathematical Subroutine Library</li>
<li>The <a href="http://www.mosek.com/">MOSEK</a> package from Erling and Knud Andersen</li>
<li>The subroutine <a href="http://netlib.org/cgi-bin/netlibfiles.pl?filename=/toms/559">HSQP</a> from John Betts, which is Algorithm 559 from the Collected Algorithms of the ACM</li>
<li>The <a href="http://www.stanford.edu/~yyye/Col.html">COPL_QP</a> package of Xiong Zhang and Yinyu Ye</li>
<li><a href="http://www.diegm.uniud.it/digaspero/index.php/software">QuadProg++</a>, a C++ solver for (strictly) convex problems from Luca Di Gaspero</li>
<li>The exact solver <a href="http://www.cgal.org/Pkg/QPSolver">QP_solver</a>, part of the Computational Geometry Algorithms Library (<a href="http://www.cgal.org/">CGAL</a>)</li>
</ul>
<p>See also Hans Mittelmann’s <a href="http://plato.asu.edu/sub/nlores.html#QP-problem">list</a> of QP solvers</p>
<p> </li>
<li><strong>Quadratic programming test examples:</strong>
<ul>
<li><a href="http://www.doc.ic.ac.uk/~im/#DATA">Maros and Meszaros’s</a> set</li>
<li>the same <a href="http://www.numerical.rl.ac.uk/cuter-www/Problems/marmes.html">problems</a> within the <a href="http://www.cse.scitech.ac.uk/nag/cuter/cuter.shtml">CUTEr</a> test set</li>
</ul>
</li>
<li>The latest version of our BiBTeX quadratic programming <a href="ftp://ftp.numerical.rl.ac.uk/pub/qpbook/qpbook.bib">bibliography</a>.</li>
<li>A paper summarizing this bibliography (<a href="ftp://ftp.numerical.rl.ac.uk/pub/qpbook/qp.ps.gz">compressed postscript</a>, <a href="ftp://ftp.numerical.rl.ac.uk/pub/qpbook/qp.pdf">PDF</a>)</li>
<li>The overheads from a talk that Nick gave on “<a href="ftp://ftp.numerical.rl.ac.uk/pub/talks/nimg.hansurlesse.3II00.ps.gz">Quadratic programming: theory and methods </a>” at the 3rd FNRS Cycle in Mathematical Programming, Han-sur-Lesse, Belgium, in February 2000.</li>
<li>The main <a href="ftp://ftp.numerical.rl.ac.uk/pub/qpbook/ZhongzhenZhang.pdf">content</a> of a book on QP by <a href="mailto:zhangzz321@126.com">Zhongzhen Zhang</a></li>
</ul>
<p><a href="http://pizi.shamoxia.com/html/y2009/155.html">http://pizi.shamoxia.com/html/y2009/155.html</a></p>
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