An online non-convex optimization problem is considered where the goal is to minimize the flow time (total delay) of a set of jobs by modulating the number of active servers, but with a switching cost associated with changing the number of active servers over time. Each job can be processed by at most one fixed speed server at any time. Compared to the usual online convex optimization (OCO) problem with switching cost, the objective function considered is non-convex and more importantly, at each time, it depends on all past decisions and not just the present one. Both worst-case and stochastic inputs are considered; for both cases, competitive algorithms are derived.

翻译：本文研究一类在线非凸优化问题，其目标是通过调节活跃服务器数量来最小化一组作业的流时间（总延迟），同时考虑因随时间改变活跃服务器数量而产生的切换成本。每个作业在任何时刻最多可由一台固定速度的服务器处理。与通常带切换成本的在线凸优化（OCO）问题相比，本文的目标函数具有非凸性，且更为关键的是，其在每个时间点不仅依赖于当前决策，还依赖于所有过往决策。本文分别考虑了最坏情形输入和随机输入，并针对两种情况推导出了竞争性算法。