  We consider online optimization problems with time-varying linear equality
constraints. In this framework, an agent makes sequential decisions using only
prior information. At every round, the agent suffers an environment-determined
loss and must satisfy time-varying constraints. Both the loss functions and the
constraints can be chosen adversarially. We propose the Online Projected
Equality-constrained Newton Method (OPEN-M) to tackle this family of problems.
We obtain sublinear dynamic regret and constraint violation bounds for OPEN-M
under mild conditions. Namely, smoothness of the loss function and boundedness
of the inverse Hessian at the optimum are required, but not convexity. Finally,
we show OPEN-M outperforms state-of-the-art online constrained optimization
algorithms in a numerical network flow application.
