We consider the optimization problem (P), α =infh(G),, whereG≠ Ø is a subset of a locally convex spaceFandh:F→R, “embedded” into a family of optimization problemswhereXis a locally convex space and φ:F×X→R.For surrogate dual, respectively. Lagrangian dual problems (Q), β = sup λ(X*), to (P),, defined with the aid of this embedding, we give necessary and sufficient conditions for α = β,involving functionals φ εX*and level sets off, respectively ofᵮ(x,t), =f(x), +t(xεX,tεR),, or involving surrogate ε-subdifferentials (which we introduce here),, respectively ε-subdifferentials off(ε ≧ 0),. We give applications to, optimization problems perturbed by multifunctions and to optimization problems for systems, obtaining conditions for surrogate duality in terms of functionals φ εX*and the level sets ofh.