# Saddle-point problem and strong duality

1. Oct 4, 2012

### lementin

Hello everyone,

Assume we have a general minimax problem
$\min\limits_{x \in X}{\max\limits_{y \in Y}{(Ax,y) \,\,+G(x) - F^*(y)} },$
where $G, \,F^*\,$ are proper, convex and lower-semicontinuous and $F^*$ is a conjugate of another function F.
The corresponding primal problem is
$\min\limits_{x \in X}{F(Ax) + G(x)}$
and the dual problem is
$\max\limits_{y \in Y}{-G^*(-A^*y) - F^*(y)}$
My question is whether there is a criterion for strong duality (something analogous to Slater's conditions for constrained optimization).