Legendre-Fenchel duality in m-convexity - Wibowo, Ratno Bagus Edy; Marjono; Pramana, Eko Dedi (KOMUNITAS Analisis Matematika INDONESIA, 2024)
The Legendre-Fenchel transform, which maps a function to its convex conjugate, provides a dual perspective that is fundamental in understanding optimization problems. In this work, we show that m-convex function in n-dimensional normed spaces can be viewed as the Legendre-Fenchel dual problem. By constructing an epi-graph of m-convexity in n-dimensional normed spaces, we obtained some properties including the Legendre transform. Particularly, we prove this for certain convex functions.