An alternative definition for c-convex functions and another synthetic statement of MTW condition
Optimization and Control
2025-10-08 v2 Analysis of PDEs
Abstract
The main theorem of this paper states that the c-convexity and the alternative c-convexity are equivalent if and only if the cost function c satisfies MTW condition. The alternative c-convex function is an analogy of the definition of the convex function that is using the inequality phi(t x1 + (1 - t) x0) <= t phi(x1) + (1 - t) phi(x0). We study properties of the alternative c-convex functions and MTW condition, then prove the main theorem.
Cite
@article{arxiv.2505.12063,
title = {An alternative definition for c-convex functions and another synthetic statement of MTW condition},
author = {Seonghyeon Jeong},
journal= {arXiv preprint arXiv:2505.12063},
year = {2025}
}
Comments
The previous version contained a few errors, and they are revised in this version