A strongly polynomial algorithm to solve combinatorial linear programs
Operations Research
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
Mathematics of Operations Research
Lower and upper bounds for the allocation problem and other nonlinear optimization problems
Mathematics of Operations Research
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
Solving certain singly constrained convex optimization problems in production planning
Operations Research Letters
A branch and search algorithm for a class of nonlinear knapsack problems
Operations Research Letters
Review of recent development: An O( n) algorithm for quadratic knapsack problems
Operations Research Letters
A pegging algorithm for the nonlinear resource allocation problem
Computers and Operations Research
A linear approximation for redundant reliability problems with multiple component choices
Computers and Industrial Engineering
Exact Algorithm for Concave Knapsack Problems: Linear Underestimation and Partition Method
Journal of Global Optimization
An approximate dynamic programming approach to convex quadratic knapsack problems
Computers and Operations Research
Journal of Global Optimization
Fully polynomial time approximation schemes for stochastic dynamic programs
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Journal of Computational and Applied Mathematics
Convergent Lagrangian and domain cut method for nonlinear knapsack problems
Computational Optimization and Applications
Joint throughput maximization and fair uplink transmission scheduling in CDMA systems
EURASIP Journal on Wireless Communications and Networking - Special issue on fairness in radio resource management for wireless networks
An approximate dynamic programming approach to convex quadratic knapsack problems
Computers and Operations Research
Server allocation algorithms for tiered systems
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Optimization over integers with robustness in cost and few constraints
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
On a nonseparable convex maximization problem with continuous knapsack constraints
Operations Research Letters
The submodular knapsack polytope
Discrete Optimization
Exact solution of a class of nonlinear knapsack problems
Operations Research Letters
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The nonlinear Knapsack problem is to minimize a separable concave objective function, subject to a single ''packing'' constraint, in nonnegative variables. We consider this problem in integer and continuous variables, and also when the packing constraint is convex. Although the nonlinear Knapsack problem appears difficult in comparison with the linear Knapsack problem, we prove that its complexity is similar. We demonstrate for the nonlinear Knapsack problem in n integer variables and knapsack volume limit B, a fully polynomial approximation scheme with running time O@?((1/@e^2) (n + 1/@e^2)) (omitting polylog terms); and for the continuous case an algorithm delivering an @e-accurate solution in O(n log(B/@e)) operations.