Explicit convex and concave envelopes through polyhedral subdivisions
Explicit convex and concave envelopes through polyhedral subdivisions
复制标题
通过多面体细分显式凸凹包络
DOI：
--
复制
发表时间：
2010
影响因子：
2.7
通讯作者：
Chuanhui Xiong
中科院分区：
文献类型：
--
作者：
Mohit Tawarmalani;Jean;Chuanhui Xiong
在本文中，我们推导了超矩形各个子集上多个非线性函数的凸包络和凹包络的显式表征。这些包络线是通过识别超矩形的多面体细分来获得的，在超矩形上可以轻松构建包络线。特别是，我们使用这些技术以封闭形式导出凹可扩展超模函数的凹包络和析取凸函数的凸包络。
In this paper, we derive explicit characterizations of convex and concave envelopes of several nonlinear functions over various subsets of a hyper-rectangle. These envelopes are obtained by identifying polyhedral subdivisions of the hyper-rectangle over which the envelopes can be constructed easily. In particular, we use these techniques to derive, in closed-form, the concave envelopes of concave-extendable supermodular functions and the convex envelopes of disjunctive convex functions.