A new duality formulation (D) for general equilibrium (EP) problems is proposed on the basis of convex optimization in locally convex vector spaces (LCVS). Assume that is a LCVS, is its continuous dual, is a convex subset of , is a mapping from in the extended reals beeing convex and lower semicontinuous in the second variable. Further assume that for all there is a such that and either or is continuous at . An optimization problem
is defined as dual problem for the equilibrium problem
where is well defined and non-positive on and is the effektive domain of . The following strong duality results are shown:
Theorem 3.1: If is a solution of (EP) then (D) has a solution and .
Theorem 3.2: (EP) is -solvable for each if and only if the optimal value of (D) is zero. It is proposed to solve (D) instead of (EP). Applications to quadratic convex-concave saddle point problems and general convex optimization problems are given.