First-Order Dynamic Optimization for Streaming Convex Costs
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2023
- DOI:
- 10.48550/arXiv.2310.07925
- arXiv:
- arXiv:2310.07925
- Bibcode:
- 2023arXiv231007925R
- Keywords:
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- Mathematics - Optimization and Control;
- Computer Science - Machine Learning