On minimax theorems for lower semicontinuous functions in Hilbert spaces
  We prove minimax theorems for lower semicontinuous functions defined on a Hilbert space. The main tool is the theory of $\Phi$-convex functions and sufficient and necessary conditions for the minimax equality to hold for $\Phi$-convex functions. These conditions are expressed in terms of abstract $\Phi$-subgradients. 
Ewa M. Bednarczuk, Monika Syga
math.OC