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Knapsack problems with sigmoid utilities: Approximation algorithms via hybrid optimization

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  • Srivastava, Vaibhav
  • Bullo, Francesco

Abstract

We study a class of non-convex optimization problems involving sigmoid functions. We show that sigmoid functions impart a combinatorial element to the optimization variables and make the global optimization computationally hard. We formulate versions of the knapsack problem, the generalized assignment problem and the bin-packing problem with sigmoid utilities. We merge approximation algorithms from discrete optimization with algorithms from continuous optimization to develop approximation algorithms for these NP-hard problems with sigmoid utilities.

Suggested Citation

  • Srivastava, Vaibhav & Bullo, Francesco, 2014. "Knapsack problems with sigmoid utilities: Approximation algorithms via hybrid optimization," European Journal of Operational Research, Elsevier, vol. 236(2), pages 488-498.
    • Handle: RePEc:eee:ejores:v:236:y:2014:i:2:p:488-498
    DOI: 10.1016/j.ejor.2013.12.035
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