On Minimax Theorems for Lower Semicontinuous Functions in Hilbert Spaces

Ewa Bednarczuk; Monika Syga

Abstract

We prove minimax theorems for lower semicontinuous functions defined on a Hilbert space. The main tools are the theory of Φ-convex functions and sufficient and necessary conditions for the minimax equality for general Φ-convex functions. The conditions we propose are expressed in terms of abstract Φ-subgradients.

Author information

Contact details are reproduced from the original publication and may be historical.

Ewa Bednarczuk

System Research Institute, Polish Academy of Sciences, Newelska 6, 01-447 Warsaw, Poland
and: Faculty of Mathematics and Information Science, Warsaw University of Technology, ul. Koszykowa 75, 00-662 Warsaw, Poland

Ewa.Bednarczuk@ibspan.waw.pl

Monika Syga

Faculty of Mathematics and Information Science, Warsaw University of Technology, ul. Koszykowa 75, 00-662 Warsaw, Poland

M.Syga@mini.pw.edu.pl

Keywords

Abstract convexity
minimax theorems
intersection property
abstract Phi-subdifferential
abstract Phi-subgradient

Mathematics Subject Classification

32F17, 49J52, 49K27, 49K35, 52A01

Suggested citation

E. Bednarczuk, M. Syga. “On Minimax Theorems for Lower Semicontinuous Functions in Hilbert Spaces.” Journal of Convex Analysis 25 (2018), No. 2, 389–402.