Cutting Plane Algorithms for Nonlinear Semi-Definite Programming Problems with Applications
Cutting Plane Algorithms for Nonlinear Semi-Definite Programming Problems with Applications
复制标题
非线性半定规划问题的割平面算法及其应用
DOI：
10.1023/a:1021985014197
复制
发表时间：
2003
影响因子：
1.8
通讯作者：
H. Tuy
中科院分区：
文献类型：
--
作者：
H. Konno;Naoya Kawadai;H. Tuy
我们将提出一个外近似（切割平面）方法，用于最小化受变量X∈Rn的半定约束的函数fX。当目标函数为线性时，已经提出了许多有效的算法。然而，当目标函数为非线性时，实用的算法很少。本文提出的算法是一种外逼近（割平面）方法，它已成功地应用于几个低秩全局优化问题，包括广义凸乘性规划问题和广义线性分式规划问题等。我们将证明当f是凸的，n是相对小的时，该算法也能很好地工作。此外，我们将提供在各种技术假设下的收敛性证明。
We will propose an outer-approximation (cutting plane) method for minimizing a function fX subject to semi-definite constraints on the variables X∈Rn. A number of efficient algorithms have been proposed when the objective function is linear. However, there are very few practical algorithms when the objective function is nonlinear. An algorithm to be proposed here is a kind of outer-approximation(cutting plane) method, which has been successfully applied to several low rank global optimization problems including generalized convex multiplicative programming problems and generalized linear fractional programming problems, etc. We will show that this algorithm works well when f is convex and n is relatively small. Also, we will provide the proof of its convergence under various technical assumptions.
使用半定 Logit 模型估计失效概率
DOI：
--
发表时间：
2004
期刊：
Journal of Computational Management Science 1
影响因子：
--
作者：
Konno;H.;Kawadai;N.;Wu;D.
通讯作者：
D.