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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi Hilbert Journal of Mathematical Analysis
Pramana, Eko Dedi
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Chemistry Control & Systems Engineering Engineering Mathematics Physics

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Journal : Hilbert Journal of Mathematical Analysis

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Legendre-Fenchel duality in m-convexity Wibowo, Ratno Bagus Edy; Marjono; Pramana, Eko Dedi
Hilbert Journal of Mathematical Analysis Vol. 2 No. 2 (2024): Hilbert J. Math. Anal.
Publisher : KOMUNITAS Analisis Matematika INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62918/hjma.v2i2.23

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.
Co-Authors Marjono Mohamad Muslikh Ratno Bagus Edy Wibowo