Capacity Provisioning Motivated Online Non-Convex Optimization Problem
  with Memory and Switching Cost
Rahul Vaze Jayakrishnan Nair
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.