The nonlinear knapsack problem
The nonlinear Knapsack problem is to maximize a separable concave objective function, subject to a single {open_quotes}packing{close_quotes} 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 knapsacks volume limit B, A psuedo-polynomial algorithm solving it optimally in O(nB{sup 2}); a fully polynomial approximation scheme with running time {tilde O}({sub {epsilon}{sup 2}}{sup 1}(n + {epsilon}2{sup 1})) (omitting polylog terms); and for the continuous case an algorithm delivering an {epsilon}-accurate solution in O(nlog (B{epsilon})) operations.
- OSTI ID:
- 36131
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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