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arXiv · 2303.07793

Nearly Convex Optimal Value Functions and Some Related Topics

Nguyen Quang Huy·Nguyen Mau Nam·Nguyen Dong Yen
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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.

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Nguyen Quang Huy, Nguyen Mau Nam, Nguyen Dong Yen. 2023-03-14. Nearly Convex Optimal Value Functions and Some Related Topics. https://arxiv.org/abs/2303.07793

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