A solution method for combined semi-infinite and semi-definite programming

A solution method for combined semi-infinite and semi-definite programming
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DOI：
10.1017/s1446181100013511
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发表时间：
2004-04
期刊：
The ANZIAM Journal
影响因子：
--
通讯作者：
Shengjie Li;Xiaoqi Yang;K. Teo;Soon-Yi Wu
Shengjie Li;Xiaoqi Yang;K. Teo;Soon-Yi Wu
中科院分区：
其他
文献类型：
--
作者：
Shengjie Li;Xiaoqi Yang;K. Teo;Soon-Yi Wu

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摘要本文给出了一类半无限半定组合规划问题的离散化算法和一种自适应格式。我们证明了该算法生成的任何点序列都包含一个收敛的子序列，并且每个聚点都是半无限半定规划问题的局部最优解。为了说明该算法的有效性，我们对两类具体问题进行了求解。它们是二次约束半无限二次规划问题和半无限特征值问题的松弛。
Abstract In this paper, we develop a discretisation algorithm with an adaptive scheme for solving a class of combined semi-infinite and semi-definite programming problems. We show that any sequence of points generated by the algorithm contains a convergent subsequence; and furthermore, each accumulation point is a local optimal solution of the combined semi-infinite and semi-definite programming problem. To illustrate the effectiveness of the algorithm, two specific classes of problems are solved. They are relaxations of quadratically constrained semi-infinite quadratic programming problems and semi-infinite eigenvalue problems.