A Saddle Value Characterization of Fan's Equilibrium Points

In this paper we develop a saddle value problem formulation for an equilibrium problem of Fan. Employing separably-infinite programming we give an equivalent dual pair of uniextremal problems for the purpose of making it easier to actually solve for the Fan equilibrium point. The uniextremal duality provides interpretations for the variables of each problem of the separably- infinite dual pair, even when they are not at their optimal values. The Fan equilibrium problem is basically a fixed point problem, and one establishes existence and uniqueness by other methods. Fixed point methods are certainly useful, perhaps even necessary for establishing existence, but it is difficult to obtain analytic information such as interpretations of the variables when they are not at their optimal values.