A Dual‐Type Method Based Algorithm for Nonlinear Large Network Optimization Problems

Abstract

ABSTRACTIn previous research, we have proposed a Dual Projected Pseudo Quasi Newton (DPPQN) method which differs from the conventional Lagrange relaxation method by treating the inequality constraints as the domain of the primal variables in the dual function and using Projection Theory to handle the inequality constraints. We have combined this dual‐type method with a Projected Jacobi (PJ) method to solve nonlinear large network optimization problems with decomposable inequality constraints, and have achieved several attractive features.To retain the attractive features and to remedy the flaw of the previous method, in the current paper, we propose an active set strategy based DPPQN method to solve the projection problem formed by coupling functional inequality constraints. This method associated with the DPPQN method and the PJ method can be used to solve general nonlinear large network optimization problems. We present this algorithm, demonstrate its computational efficiency through numerical simulations and compare it with the previous method.