Augmented Lagrangian algorithms for solving the continuous nonlinear resource allocation problem

Abstract

We propose a class of algorithms for solving the continuous nonlinear resource allocation problem which is stated many times in the literature as the Knapsack problem. This problem is known for its diverse gamma of applications and we solve it by using a hybrid approach, i.e., we combine the augmented Lagrangian method with Newton’s method to solve the subproblem generated by it. In other words, at each step we minimize the augment ed Lagrangian using Newton’s method and project the solution on the box. Most of the papers in this area deal with quadratic separable problems. Our proposal is more general in the sense that the problem can be non-quadratic and non-separable. We present and discuss the convergence properties for the proposed method and we show numerical applications illustrating its competitiveness and robustness for solving different Knapsack problems.