ε-Optimality in Reverse Optimization

The purpose of this paper is to completely characterize the global approximate optimality (ε-optimality) in reverse convex optimization under the general nonconvex constraint "h(x) ≥ 0". The main condition presented is obtained in terms of Fenchel's ε-subdifferentials thanks to El Maghri's ε-efficiency in difference vector optimization [J. Glob. Optim. 61 (2015) 803--812], after converting the reverse convex program into a DC bicriteria program. This extends and improves similar results from the literature dealing with exact (ε=0) solutions. In fact, our main result also applies to reverse convex programs subject to additional convex constraints as well as the particular case of convex problems under nonlinear equality constraint "h(x) = 0".

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Hassan II University, Casablanca, Morocco, March 15, 2024.

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