Monotone Mapping

A mapping \( \phi \) is monotone if for all \( x,y \in \text{dom}\phi\),

\[(x-y)^T(\phi(x)-\phi(y))\geq0\]

 

Reference:

• Boyd, S. P., & Vandenberghe, L. (2004). Convex optimization. Cambridge university press.
• Khanh, P., Luong, H. C., Mordukhovich, B., & Tran, D. (2024). Fundamental convergence analysis of sharpness-aware minimization. Advances in Neural Information Processing Systems, 37, 13149-13182.