I have a convex optimization problem and I am trying to solve it using lagrange duality method. For one of the solutions of my problem, negative values are obtained for some the lagrange multipliers. My question is: this solution is not optimal or not feasible? Indeed I want to know what does a negative lagrange multiplier imply? What if we find a solution to the original problem which yields some negative lagrange multipliers?
Answer: I think I have found the answer to my question. If a Lagrange Multiplier is computed as negative, its associated constraint is redundant, i.e., the optimal solution with and without that constraint is the same.