The nonlinear knapsack problem is a bounded nonlinear integer programming problem that maximizes a separable function subject to separable constraints. In this talk we present a convergent Lagrangian and domain cut method for solving this kind of problems. The method exploits the special structure of the problem by Lagrangian decomposition and dual search. The domain cut is used to eliminate the duality gap and thus to guarantee the convergence of the algorithm. The algorithm is first motivated and developed for the singly constrained nonlinear knapsack problems and is then extended to multi-dimensional nonlinear knapsack problems via subgradient method and a constraint surrogate technique. Computational results are reported for a variety of nonlinear knapsack problems with up to 2000 integer variables.
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