An Online Newton’s Method for Time-Varying Linear Equality Constraints

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 suffers environment-determined loss and must satisfy Both functions constraints can be chosen adversarially. propose Online Projected Equality-constrained Newton Method (OPEN-M) to tackle family of problems. obtain sublinear dynamic regret constraint violation bounds for OPEN-M under mild conditions. Namely, smoothness function boundedness inverse Hessian at optimum are required, but not convexity. Finally, we show outperforms state-of-the-art constrained algorithms in a numerical network flow application.