A nonlinear minimax allocation problem with multiple knapsack constraints

A nonlinear minimax allocation problem with multiple knapsack constraints

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Article ID: iaor19921
Country: Netherlands
Volume: 10
Issue: 4
Start Page Number: 183
End Page Number: 187
Publication Date: Jun 1991
Journal: Operations Research Letters
Authors:
Abstract:

A nonlinear minimax allocation problem with multiple knapsack-type resource constraints is considered. Each term in the objective function is a nonlinear, strictly decreasing and continuous function of a single variable. All variables are continuous and nonnegative. A previous algorithm for such problems repeatedly solves relaxed problems without the nonnegativity constraints. That algorithm is particularly efficient for certain nonlinear functions for which there are closed-form solutions for the relaxed problems; for other functions, however, the algorithm must employ search methods. A new algorithm is presented, that uses at each iteration simple-to-compute algebraic expressions to check optimality conditions, instead of solving the relaxed minimax problems. The new algorithm is therefore significantly more efficient for more general nonlinear functions.

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