Classic Lagrangian may not be applicable to the traveling salesman problem
arXiv:1405.1298
Abstract
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.
7 pages