Nonlinear Lagrange duality theorems and penalty function methods in continuous optimization

We propose a general dual program for a constrained optimization problem via generalized nonlinear Lagrangian functions. Our dual program includes a class of general dual programs with explicit structures as special cases. Duality theorems with the zero duality gap are proved under very general assumptions and several important corollaries which include some known result are given. Using dual functions as penalty functions, we also establish that a sequence of approximate optimal solutions of the penalty function converges to the optimal solution of the original optimization problem.