SparsePOP: a Sparse Semidefinite Programming Relaxation of Polynomial Optimization Problems
SparsePOP: a Sparse Semidefinite Programming Relaxation of Polynomial Optimization Problems
复制标题
DOI：
--
复制
发表时间：
2005
影响因子：
4
通讯作者：
Hayato Waki;Sunyoung Kim;M. Kojima;M. Muramatsu
中科院分区：
文献类型：
--
作者：
Hayato Waki;Sunyoung Kim;M. Kojima;M. Muramatsu
SparesPOP是稀疏半定规划（SDP）松弛方法的MATLAB实现，用于近似Waki，Kim，Kojima和Muramatsu提出的多项式优化问题（POP）的全局最优解。稀疏SDP松弛利用了稀疏结构的多项式在持久性有机污染物时，应用“层次结构的线性矩阵不等式松弛的维数增加”的拉瑟尔。从而提高了SparsePOP逼近POP最优解的效率，并且可以处理更大规模的POP。为了进行数字比较，可在http：//www.is.titech.ac.jp/Jakokojima/SparsePOP上查阅文献中的一套持久性有机污染物测试集，也可从该网站下载软件包SparesPOP。
SparesPOP is a MATLAB implementation of the sparse semidefinite programming (SDP) relaxation method for approximating a global optimal solution of a polynomial optimization problem (POP) proposed by Waki, Kim, Kojima and Muramatsu. The sparse SDP relaxation exploits a sparse structure of polynomials in POPs when applying “a hierarchy of LMI relaxations of increasing dimensions” by Lasserre. The efficiency of SparsePOP to approximate optimal solutions of POPs is thus increased, and larger scale POPs can be handled. For numerical comparison, a test set of POPs from the literature are available at http://www.is.titech.ac.jp/∼kojima/SparsePOP where the software package SparesPOP can also be downloaded.