Solving NP-hard problem using a new relaxation of approximate methods

A new approach has been introduced for solving NP-hardness problem in combinatorial optimization problems. Actully, our study focused on the relationship between the Lagrange method and Penalty method ,this paper  introduce a new relaxation of the fesible region.Furthermore, NP hard problem has been tested and showed that the Augmented Lagrangian Approach outperformed the Penalty method. Finally, our study focuses on enhancing the theoretical convergence features as well as numerical computing