The exponential barrier programming, as an analytical approximation of the linear programming

We presented a special convex programming problem as an analytical approximation of the standard linear programming problem with arbitrary accuracy. The compatibility condition of linear programming problem is perturbed and the cotangent hyperbolic function is used as an equilibrium function. It leads to a convex programming problem with parameters α, β, called Exponential Barrier Programming problem (EP (α, β)). The following statement is proved: if αβ → 0 then EP (α, β) → LP, moreover a simple proof is given on the duality theory of EP (α, β).