SDPPACK User''s Guide -- Version 0.9 Beta for Matlab 5.0.
SDPPACK User''s Guide -- Version 0.9 Beta for Matlab 5.0.
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发表时间：
1997-06
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通讯作者：
F. Alizadeh;J. Haeberly;M. V. Nayakkankuppa;M. Overton;S. Schmieta
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作者：
F. Alizadeh;J. Haeberly;M. V. Nayakkankuppa;M. Overton;S. Schmieta
本报告描述了Matlab 5.0的SDPpack 0.9 Beta版。此版本将以前的半定规划（SDP）版本扩展到混合半定-二次-线性规划（SQLP），即半定锥、二次锥和非负正交点乘积上的线性优化问题。这些锥一起构成实数上所有可能的齐次自对偶锥。主程序实现了基于XZ+ZX搜索方向的原始-对偶Mehrotra预测-校正方案。更专业的例程也可以使用，一个只解决带有对角约束的SDP，一个计算图的Lov\“asz $\theta$函数，两者都使用XZ搜索方向。我们还提供了一些方法来确定SQLP在其解处是原始退化还是对偶退化，以及严格互补性是否在那里成立。原始非简并性与对偶唯一性和对偶非简并性与原始唯一性相关联，尽管如果严格互补性不成立，这些条件就不等价。还提供了一个例程来计算SQLP的条件数。Matlab代码调用mex文件以提高性能;二进制文件可用于多种平台。基准测试表明，
This report describes SDPpack Version 0.9 Beta for Matlab 5.0. This version extends the previous release for semidefinite programming (SDP) to mixed semidefinite--quadratic--linear programs (SQLP), i.e.\ linear optimization problems over a product of semidefinite cones, quadratic cones and the nonnegative orthant. Together, these cones make up all possible homogeneous self-dual cones over the reals. The main routine implements a primal--dual Mehrotra predictor--corrector scheme based on the XZ+ZX search direction for SDP. More specialized routines are also available, one to solve SDP''s with diagonal constraints only, and one to compute the Lov\''asz $\theta$ function of a graph, both using the XZ search direction. Routines are also provided to determine whether an SQLP is primal or dual degenerate at its solution and whether strict complementarity holds there. Primal nondegeneracy is associated with dual uniqueness and dual nondegeneracy with primal uniqueness, though these conditions are not equivalent if strict complementarity fails to hold. A routine is also provided to compute the condition number of an SQLP. The Matlab code calls mex files for improved performance; binaries are available for several platforms. Benchmarks show that the codes