First-Order Dynamic Optimization for Streaming Convex Costs
M. Rostami H. Moradian S. S. Kia
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.