Mathematical Programming Computational for Solving NP-Hardness Problem
Ahmed Hasan Alridha, Ahmed Sabah Al-Jilawi
Abstract
Abstract In this paper we will introduce a new approach for solving K-cluster problem which is one of the NP-hardness problem, in combinatorial optimization problems. In addition, P is NP-hardness if and only if the polynomial time of each NP problem is reduced to P. Actually, our study was focused on the two methods which is Penalty and Augmented Lagrangian methods base on the numerical result. Moreover, we tested the K-cluster problem and found the Augmented Lagrangian Method faster than Penalty method. Finally, our research is not just focus on the numerical computational but also improving the theoretical converges properties.
Topics & Concepts
Augmented Lagrangian methodFocus (optics)Mathematical optimizationComputational complexity theoryLagrangianMathematicsCluster (spacecraft)Time complexityComputer scienceAlgorithmApplied mathematicsPhysicsProgramming languageOpticsAdvanced Optimization Algorithms ResearchStochastic Gradient Optimization TechniquesOptimization and Packing Problems