Legendre-Fenchel duality in m-convexity

Ratno Bagus Edy Wibowo; Marjono; Eko Dedi Pramana

doi:10.62918/hjma.v2i2.23

Authors

Ratno Bagus Edy Wibowo Universitas Brawijaya
Marjono Universitas Brawijaya
Eko Dedi Pramana Universitas Brawijaya

DOI:

https://doi.org/10.62918/hjma.v2i2.23

Keywords:

Dual, Convex, m-convex, Legendre-Fenchel, Optimization

Abstract

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.

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