持久资产切换对一类混合启发优化算法的影响分析
Analyzing the Effect of Persistent Asset Switches on a Class of Hybrid-Inspired Optimization Algorithms
摘要：
凸优化的挑战是目前普遍存在于许多科学和工程领域。在凸优化的许多应用中，例如涉及多代理系统和资源分配的应用，目标函数可以在优化算法的执行期间持续切换。出于这样的应用程序，我们分析了连续时间优化算法中持续切换目标的效果。特别是，我们利用现有的鲁棒稳定性结果切换系统具有不同的平衡，并将这些结果扩展到微分包含所描述的系统，使结果适用于最近的优化算法，采用微分包含，以提高效率和/或鲁棒性。在混杂系统理论的框架内，我们提供了一个准确的表征，在欧米茄极限集，一组的优化动态收敛。最后，通过考虑开关信号被约束在其平均停留时间，我们建立了半全局实际渐近稳定的这些集的停留时间参数。
英文摘要：
Convex optimization challenges are currently pervasive in many science and engineering domains. In many applications of convex optimization, such as those involving multi-agent systems and resource allocation, the objective function can persistently switch during the execution of an optimization algorithm. Motivated by such applications, we analyze the effect of persistently switching objectives in continuous-time optimization algorithms. In particular, we take advantage of existing robust stability results for switched systems with distinct equilibria and extend these results to systems described by differential inclusions, making the results applicable to recent optimization algorithms that employ differential inclusions for improving efficiency and/or robustness. Within the framework of hybrid systems theory, we provide an accurate characterization, in terms of Omega-limit sets, of the set to which the optimization dynamics converge. Finally, by considering the switching signal to be constrained in its average dwell time, we establish semi-global practical asymptotic stability of these sets with respect to the dwell-time parameter.
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