V2EX bilevel programming

Bilevel Programming

定义 Definition

双层规划:一种包含“上下两层”优化问题的数学规划框架。上层(领导者)选择决策变量时,必须考虑下层(跟随者)会在给定上层决策下自行求解其优化问题;因此,上层约束通常隐含了下层的最优反应。常用于定价需求网络设计流量分配政策制定市场反应等场景。(该术语在不同文献中也常与 bilevel optimization 互用。)

发音 Pronunciation (IPA)

/balvl prorm/

例句 Examples

The team used bilevel programming to model a leader and a follower making decisions.
团队使用双层规划来刻画一个领导者与一个跟随者的决策过程。

In transportation planning, bilevel programming can capture how a city sets tolls while drivers adjust their routes to minimize travel time and cost.
在交通规划中,双层规划可以表达城市制定收费策略,而驾驶者会调整路线以最小化出行时间与费用。

词源 Etymology

bilevelbi-(“两、双”)+ level(“层级”)构成,字面意思是“两层的”;programming 在运筹学语境中指“(数学)规划/优化”。“双层规划”这一概念与领导者跟随者(Stackelberg)式的层级决策密切相关,后来在运筹学与优化理论中发展为系统化的双层优化模型。

相关词 Related Words

文学与著作中的用例 Literary Works

  • Stephan Dempe, Foundations of Bilevel Programming(系统阐述双层规划的理论基础与算法)
  • Jonathan F. Bard, Practical Bilevel Optimization: Algorithms and Applications(强调应用场景与可实现的求解方法)
  • B. Colson, P. Marcotte, G. Savard, “Bilevel programming: A survey”(综述性论文,汇总模型、性质与算法进展)
  • Heinrich von Stackelberg, Market Structure and Equilibrium(与“领导者跟随者”思想相关的经典来源,虽未必以该术语命名但为重要理论背景)
关于     帮助文档     自助推广系统     博客     API     FAQ     Solana     1792 人在线   最高记录 6679       Select Language
创意工作者们的社区
World is powered by solitude
VERSION: 3.9.8.5 6s UTC 06:07 PVG 14:07 LAX 22:07 JFK 01:07
Do have faith in what you're doing.
ubao msn snddm index pchome yahoo rakuten mypaper meadowduck bidyahoo youbao zxmzxm asda bnvcg cvbfg dfscv mmhjk xxddc yybgb zznbn ccubao uaitu acv GXCV ET GDG YH FG BCVB FJFH CBRE CBC GDG ET54 WRWR RWER WREW WRWER RWER SDG EW SF DSFSF fbbs ubao fhd dfg ewr dg df ewwr ewwr et ruyut utut dfg fgd gdfgt etg dfgt dfgd ert4 gd fgg wr 235 wer3 we vsdf sdf gdf ert xcv sdf rwer hfd dfg cvb rwf afb dfh jgh bmn lgh rty gfds cxv xcv xcs vdas fdf fgd cv sdf tert sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf sdf shasha9178 shasha9178 shasha9178 shasha9178 shasha9178 liflif2 liflif2 liflif2 liflif2 liflif2 liblib3 liblib3 liblib3 liblib3 liblib3 zhazha444 zhazha444 zhazha444 zhazha444 zhazha444 dende5 dende denden denden2 denden21 fenfen9 fenf619 fen619 fenfe9 fe619 sdf sdf sdf sdf sdf zhazh90 zhazh0 zhaa50 zha90 zh590 zho zhoz zhozh zhozho zhozho2 lislis lls95 lili95 lils5 liss9 sdf0ty987 sdft876 sdft9876 sdf09876 sd0t9876 sdf0ty98 sdf0976 sdf0ty986 sdf0ty96 sdf0t76 sdf0876 df0ty98 sf0t876 sd0ty76 sdy76 sdf76 sdf0t76 sdf0ty9 sdf0ty98 sdf0ty987 sdf0ty98 sdf6676 sdf876 sd876 sd876 sdf6 sdf6 sdf9876 sdf0t sdf06 sdf0ty9776 sdf0ty9776 sdf0ty76 sdf8876 sdf0t sd6 sdf06 s688876 sd688 sdf86