Classic Lagrangian may not be applicable to the traveling salesman   problem
  In this short note, the dual problem for the traveling salesman problem is constructed through the classic Lagrangian. The existence of optimality conditions is expressed as a corresponding inverse problem. A general 4-cities instance is given, and the numerical experiment shows that the classic Lagrangian may not be applicable to the traveling salesman problem. 
Michael X. Zhou
cs.DS