On a discrete nonlinear and nonseparable knapsack problem

In this paper, a discrete knapsack problem with a convex but nonseparable objective function is considered. Relaxing the discrete requirements (and assuming nonnegativity), we show how the resulting problem can be solved by an efficient algorithm which solves a series of quadratic knapsack problems in O( n) time. This algorithm forms the basis for a branch-and-bound algorithm, which is subsequently used to test the efficacy of a proposed heuristic. Computational results are presented.