| 两个凸多面体的差及几种次微分之间的关系 |
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| 引用本文： | 高岩. 两个凸多面体的差及几种次微分之间的关系[J]. 运筹学学报, 2000, 4(3): 57-66 |
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| 作者姓名： | 高岩 |
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| 作者单位： | 中国矿业大学北京校区,北京100083 |
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| 摘 要： | 给出两种两个凸多面体差的表达式，利用这些表达式，可以具体计算这两种凸多面体的差，做为应用讨论了利用拟微分计算Penot微分和Clarke广义梯度，特别讨论了一类非光滑函数，极大值函数的光滑复合。
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| 关 键 词： | 非光滑优化 凸多面体 次微分 差 拟微分 CLARKE广义梯度 PENOT微分 |
| 修稿时间： | 1999-11-10 |
Differences of Two Convex Polyhedrons and Relations among Various Subdifferentials |
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| YAN GAO. Differences of Two Convex Polyhedrons and Relations among Various Subdifferentials[J]. OR Transactions, 2000, 4(3): 57-66 |
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| Authors: | YAN GAO |
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| Affiliation: | YAN GAO(China University of Mining and Technology-Beijing, Beijing 100083, China) |
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| Abstract: | The formulae of two difference operations of two polyhedrons, are proposed. Using these formulae, the two differences for two polyhedrons could be calculated. As applications, calculation of Penot differential and estimation of Clarke generalized gradient via quasidifferential are discussed. Particularly, a class of nonsmooth function, smooth compositions of max-type functions is investigated in detail. |
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| Keywords: | nonsmooth optimization difference of two convex compact sets quasidifferential Clarke generalized gradient Penot differential. |
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