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Saddle-point problem and strong duality

  1. Oct 4, 2012 #1
    Hello everyone,

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