Discrete Filled Function Method for Discrete Global Optimization
Computational Optimization and Applications
Generalized Nonlinear Lagrangian Formulation for Bounded Integer Programming
Journal of Global Optimization
Discrete global descent method for discrete global optimization and nonlinear integer programming
Journal of Global Optimization
Journal of Global Optimization
Convergent Lagrangian and domain cut method for nonlinear knapsack problems
Computational Optimization and Applications
A nonlinear Lagrangian dual for integer programming
Operations Research Letters
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A logarithmic-exponential dual formulation is proposed in this paper for bounded integer programming problems. This new dual formulation possesses an asymptotic strong duality property and guarantees the identification of an optimal solution of the primal problem. These prominent features are achieved by exploring a novel nonlinear Lagrangian function, deriving an asymptotic zero duality gap, investigating the unimodality of the associated dual function and ensuring the primal feasibility of optimal solutions in the dual formulation. One other feature of the logarithmicexponential dual formulation is that no actual dual search is needed when parameters are set above certain threshold-values.