Nearly Convex Optimal Value Functions and Some Related Topics
Optimization and Control
2023-03-15 v1
Abstract
In this paper, we introduce new properties of the relative interior calculus for nearly convex sets, functions, and set-valued mappings. These properties are important for the development of duality theory in optimization. Then we investigate optimal value functions defined by nearly convex functions and nearly convex set-valued mappings, and derive the near convexity of the optimal value function under a qualification condition. We also develop formulas for subgradients and Fenchel conjugates of this class of functions, and explore their applications to duality theory.
Keywords
Cite
@article{arxiv.2303.07793,
title = {Nearly Convex Optimal Value Functions and Some Related Topics},
author = {Nguyen Quang Huy and Nguyen Mau Nam and Nguyen Dong Yen},
journal= {arXiv preprint arXiv:2303.07793},
year = {2023}
}