权重平衡有向网络下分布式约束优化的连续时间算法设计

本文研究权重平衡有向网络下分布式约束优化问题的求解,其中网络的全局目标函数是由每个智能体的局部目标函数的和构成,全局的约束是由每个智能体的局部约束的交构成.为了分布式求解该问题的最优解,首先引入智能体的局部共轭函数将其转换为Fenchel对偶问题.其次,从Fenchel对偶问题出发,提出一类基于奇异摄动系统的分布式连续时间算法.在局部目标函数和其梯度分别满足强凸和Lipschitz（李普希兹）连续的情况下,结合凸分析方法和Lyapunov（李雅普诺夫）稳定性理论,结果表明所提算法能够获得原问题和对偶问题的最优值.最后,数值仿真进一步验证了所提算法的有效性.     

Including friction in the mathematics of classical plasticity

In classical plasticity there are clear mathematical links between the dissipation function and the consequent yield function and flow rule. These links help to construct constitutive equations with the minimum of adjustable parameters. Modelling granular materials, however, requires that the dissipation function depends on the current stress state (frictional plasticity) and this changes the mathematical structure—altering the links and invalidating the associated flow rule. In this paper we show, for a large family of dissipation functions, how much of the structure remains intact when frictional dissipation is included. The surviving links are examined using straightforward physically based graphical insight and well‐established mathematical techniques leading to a central result, which provides a mathematical justification for the procedural features of hyperplasticity. This should allow hyperplasticity to be used more widely and certainly with increased confidence. As an example of the effectiveness of the general method, two specific dissipation functions are constructed from the simple physical concepts of sliding friction and granule damage. One is based on a Drucker–Prager cone and the other a Matsuoka–Nakai cone, both incorporate kinematic hardening and a compactive cap. In each Case a single smooth yield function with consistent flow rules is produced. The computational usefulness of an inequality derived in the paper is demonstrated in the generation of the figures showing yield surfaces and flow directions by means of a simple maximization procedure. Copyright © 2009 John Wiley & Sons, Ltd.