Minimization methods for non-differentiable functions
Minimization methods for non-differentiable functions
Discrete optimization
Resource allocation problems: algorithmic approaches
Resource allocation problems: algorithmic approaches
Convex separable optimization is not much harder than linear optimization
Journal of the ACM (JACM)
Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Lagrangian decomposition for integer nonlinear programming with linear constraints
Mathematical Programming: Series A and B
Mathematics of Operations Research
A pegging algorithm for the nonlinear resource allocation problem
Computers and Operations Research
Monotonic Optimization: Problems and Solution Approaches
SIAM Journal on Optimization
New bundle methods for solving Lagrangian relaxation dual problems
Journal of Optimization Theory and Applications
Success Guarantee of Dual Search in Integer Programming: p-th Power Lagrangian Method
Journal of Global Optimization
Convexification and Global Optimization in Continuous And
Convexification and Global Optimization in Continuous And
Algorithms for Separable Nonlinear Resource Allocation Problems
Operations Research
Operations Research Letters
Bounding the shared resource load for the performance analysis of multiprocessor systems
Proceedings of the Conference on Design, Automation and Test in Europe
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The nonlinear knapsack problem, which has been widely studied in the OR literature, is a bounded nonlinear integer programming problem that maximizes a separable nondecreasing function subject to separable nondecreasing constraints. In this paper we develop a convergent Lagrangian and domain cut method for solving this kind of problems. The proposed 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 finding of an optimal exact solution to the primal problem. The algorithm is first motivated and developed for singly constrained nonlinear knapsack problems and is then extended to multiply constrained nonlinear knapsack problems. Computational results are presented for a variety of medium- or large-size nonlinear knapsack problems. Comparison results with other existing methods are also reported.