First-Order Dynamic Optimization for Streaming Convex Costs
This work addresses optimization challenges in dynamic systems for applications such as control, but it appears incremental as it builds on existing methods for time-varying costs.
The paper tackles the problem of convex optimization with time-varying streaming cost functions by proposing first-order algorithms that track the optimal solution with bounded error, demonstrating computational efficiency compared to gradient descent and applying it to examples like model predictive control.
This paper proposes a set of novel optimization algorithms for solving a class of convex optimization problems with time-varying streaming cost function. We develop an approach to track the optimal solution with a bounded error. Unlike the existing results, our algorithm is executed only by using the first-order derivatives of the cost function which makes it computationally efficient for optimization with time-varying cost function. We compare our algorithms to the gradient descent algorithm and show why gradient descent is not an effective solution for optimization problems with time-varying cost. Several examples including solving a model predictive control problem cast as a convex optimization problem with a streaming time-varying cost function demonstrate our results.