Journal of Convex Analysis 27 (2020), No. 4, 1091--1098
Copyright Heldermann Verlag 2020
Barrier Functions in Subdifferential Theory
Milen Ivanov
Radiant Life Technologies Ltd., Nicosia, Cyprus
milen@radiant-life-technologies.com
Nadia Zlateva
Faculty of Mathematics and Informatics, Sofia University, Sofia, Bulgaria
zlateva@fmi.uni-sofia.bg
We present a new method for proving Correa-Jofré-Thibault's theorem that monotonicity of subdifferential implies convexity of the function. This new method is based on barrier functions. Barrier functions help overcome some of the main technical difficulties when working with lower semicontinuous functions.
Keywords: Subdifferential, monotonicity, convex function, barrier function.
MSC: 49J52, 47H05, 52A41.
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