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：本文研究一个在线非凸优化问题，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），但需考虑随时间改变活跃服务器数量所产生的切换成本。每个作业在任何时刻最多可由一个固定速度的服务器处理。与常见的带切换成本的在线凸优化（OCO）问题相比，本文考虑的目标函数是非凸的，且更重要的是，它在每个时刻依赖于所有历史决策，而不仅仅是当前决策。研究同时考虑了最坏情况输入与随机输入；针对这两种情况，均提出了具有竞争性的算法。