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A unified method for a class of convex separable nonlinear knapsack problems
Authors:Bin Zhang  Zhongsheng Hua
Affiliation:School of Management, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Abstract:In this paper, a unified algorithm is proposed for solving a class of convex separable nonlinear knapsack problems, which are characterized by positive marginal cost (PMC) and increasing marginal loss–cost ratio (IMLCR). By taking advantage of these two characteristics, the proposed algorithm is applicable to the problem with equality or inequality constraints. In contrast to the methods based on Karush–Kuhn–Tucker (KKT) conditions, our approach has linear computation complexity. Numerical results are reported to demonstrate the efficacy of the proposed algorithm for different problems.
Keywords:Nonlinear knapsack problem   Convex programming   Separable programming   Singly constrained program
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