Stability of primal-dual gradient dynamics and applications to network optimization
Stability of primal-dual gradient dynamics and applications to network optimization
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DOI：
10.1016/j.automatica.2010.08.011
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发表时间：
2010-12
期刊：
影响因子：
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通讯作者：
Diego Feijer;F. Paganini
中科院分区：
文献类型：
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作者：
Diego Feijer;F. Paganini
本文考虑动态法律寻求鞍点的两个向量变量的函数，通过移动每个在相应的部分梯度的方向。这种方法有古老的根源，在经典的工作阿罗，Hurwicz和Uzawa凸优化，并已看到其最近的应用在通信网络中的资源分配新的兴趣。本文带来了其他工具来承担这个问题，特别是Krasovskii的方法来寻找李雅普诺夫函数，并在最近获得的扩展的拉萨尔不变性原则的混合动力系统。这些方法被用来获得这些原始-对偶法律在不同的情况下的稳定性证明，并展示跨层网络优化的应用。
This paper considers dynamic laws that seek a saddle point of a function of two vector variables, by moving each in the direction of the corresponding partial gradient. This method has old roots in the classical work of Arrow, Hurwicz and Uzawa on convex optimization, and has seen renewed interest with its recent application to resource allocation in communication networks. This paper brings other tools to bear on this problem, in particular Krasovskii’s method to find Lyapunov functions, and recently obtained extensions of the LaSalle invariance principle for hybrid systems. These methods are used to obtain stability proofs of these primal–dual laws in different scenarios, and applications to cross-layer network optimization are exhibited.