Potential-Function Proofs for First-Order Methods
arXiv:1712.04581v331 citations
Originality Synthesis-oriented
AI Analysis
This work provides a theoretical framework for convergence proofs in optimization, which is incremental as it builds on existing methods without introducing new algorithms.
The paper tackles the problem of proving convergence for first-order optimization methods by using potential-function arguments, covering gradient descent, mirror descent, and accelerated variants, but does not report specific numerical results.
This note discusses proofs for convergence of first-order methods based on simple potential-function arguments. We cover methods like gradient descent (for both smooth and non-smooth settings), mirror descent, and some accelerated variants.