On the implementation of SDPT3 (version 3.1) - a MATLAB software package for semidefinite-quadratic-linear programming

2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508) Pub Date : 2004-09-02 DOI:10.1109/CACSD.2004.1393891

K. Toh, R. Tütüncü, M. Todd

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引用次数: 46

Abstract

This code is designed to solve conic programming problems whose constraint cone is a product of semidefinite cones, second-order cones, nonnegative orthants and Euclidean spaces. It employs a primal-dual predictor-corrector path-following method, with either the HKM or the NT search direction. The basic code is written in MATLAB, but key subroutines in Fortran and C are incorporated via a Mex interface. Routines are provided to read in problems in either SDPA or SeDuMi format. Sparsity and block diagonal structure are exploited, but the latter needs to be given explicitly or detected via a subroutine that is provided. Various techniques to improve the efficiency and stablity of the algorithm are incorporated. For example, step-lengths associated with semidefinite cones are calculated via the Lanczos method. Numerical experiments show that this general purpose code can solve 80% of a total of about 300 problems to an accuracy of at least 10-6 in relative duality gap and infeasibilities

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关于SDPT3(3.1版)的实现-一个半定二次线性规划的MATLAB软件包

该程序用于求解约束锥是半定锥、二阶锥、非负对角和欧氏空间乘积的二次规划问题。它采用原始对偶预测校正路径跟踪方法，使用HKM或NT搜索方向。基本代码是用MATLAB编写的，但关键的子程序是通过一个Mex接口用Fortran和C编写的。提供了SDPA或SeDuMi格式的例程来读入问题。稀疏性和块对角结构被利用，但后者需要显式给定或通过提供的子例程检测。采用了各种技术来提高算法的效率和稳定性。例如，通过Lanczos方法计算与半定锥相关的步长。数值实验表明，该通用代码可以解决总共约300个问题中的80%，在相对对偶差距和不可行性方面的精度至少为10-6

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2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508)

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