A generalized Weber problem with different gauges for different regions
A generalized Weber problem with different gauges for different regions
复制标题
不同地区采用不同规格的广义韦伯问题
DOI：
10.1016/j.amc.2014.07.005
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发表时间：
2014-10
影响因子：
4
通讯作者：
Zhu, Xiao-xing
中科院分区：
文献类型：
--
作者：
Jiang, Jian-lin;Luan, Fei;Wang, Li-ping;Zhu, Xiao-xing
本文考虑平面上的广义变分Weber问题，其中一条直线将平面分成两个区域，在不同区域内采用不同的量规来测量距离。GVWP是韦伯问题在以下几个方面的推广：(1)同时考虑了无约束和约束问题；(2)用更一般的测距函数来测量距离，而不是通常使用的L p范数。因此，GVWP在实践中更具实用性和适用性。GVWP和VWP一样是非凸的，并且作为一个广义问题比后者复杂得多。本文将GVWP问题分解为三个子问题进行最优解：将两个子问题转化为单调线性变分不等式(LVIS)，然后用投影-压缩方法求解；将第三个子问题分解为若干凸问题，并用黄金分割搜索法进行求解。通过将GVWP问题分解为三个子问题，并对这些子问题进行优化求解，提出了一种求解GVWP全局最优解的算法。初步的数值结果验证了该算法的有效性。
This paper considers a generalized variation of the Weber problem (GVWP) on the plane in which a straight line divides the plane into two regions and different gauges are employed to measure the distances in different regions. GVWP is a generalized problem of some well-studied variations of Weber problem (VWP) in the following aspects:(1) both the unconstrained and constrained problems are taken into consideration;(2) the more general distance measuring functions, gauges, are employed to measure distances instead of the usually used l p-norms. Therefore, the GVWP is more practical and applicable in practice. GVWP is nonconvex as VWP, and as a generalized problem it is more complex than the latter. In this paper the GVWP is divided into three subproblems which are optimally solved: two subproblems are reformulated into monotone linear variational inequalities (LVIs) and then solved by a projection–contraction method, while the third subproblem is divided into some convex problems and the golden section search is used to solve them. By dividing the GVWP into three subproblems and solving these subproblems optimally, an algorithm which can obtain the global optimal solution of GVWP is proposed. Preliminary numerical results are reported to verify the evident effectiveness of the proposed algorithm.
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DOI：
10.2478/agms-2013-0004
发表时间：
2013-06
期刊：
--
影响因子：
--
作者：
A. Mennucci
通讯作者：
A. Mennucci
影响因子：
5.4
作者：
LOVE, RF;MORRIS, JG
通讯作者：
MORRIS, JG
影响因子：
1.9
作者：
M. Cera;J. A. Mesa;F. Ortega;F. Plastria
通讯作者：
M. Cera;J. A. Mesa;F. Ortega;F. Plastria
DOI：
10.1016/j.amc.2013.01.067
发表时间：
2013-03
期刊：
Appl. Math. Comput.
影响因子：
--
作者：
A. Bnouhachem;H. Benazza;M. Khalfaoui
通讯作者：
A. Bnouhachem;H. Benazza;M. Khalfaoui
DOI：
10.1007/b97543
发表时间：
2003
期刊：
--
影响因子：
--
作者：
F. Facchinei;J. Pang
通讯作者：
F. Facchinei;J. Pang