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An unconstrained optimization problem is NP-hard given an oracle representation of its objective function: a technical note

Authors:

T. C. E. Cheng,

Mikhail Y. KovalyovAuthors Info & Claims

Computers and Operations Research, Volume 29, Issue 14

Pages 2087 - 2091

https://doi.org/10.1016/S0305-0548(02)00065-5

Published: 01 December 2002 Publication History

Abstract

The problem of unconstrained minimization of a piecewise linear function of one variable is shown to be NP-hard given an oracle representation of the function. This result can be applied to establish the NP-hardness of the scheduling problem with controllable job processing times given an oracle representation of the scheduling cost. The computational complexity of this scheduling problem has remained unknown for more than 20 years.

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Cited By

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Kent CLi JBlanchet JGlynn PRanzato MBeygelzimer ADauphin YLiang PVaughan J(2021)Modified frank wolfe in probability spaceProceedings of the 35th International Conference on Neural Information Processing Systems10.5555/3540261.3541368(14448-14462)Online publication date: 6-Dec-2021
https://dl.acm.org/doi/10.5555/3540261.3541368
Wang G(2004)A novel method for parameter optimization in two-dimensional dynamical modelsProceedings of the 5th WSEAS International Conference on Applied Mathematics10.5555/1378446.1378484(1-9)Online publication date: 21-Apr-2004
https://dl.acm.org/doi/10.5555/1378446.1378484

Index Terms

An unconstrained optimization problem is NP-hard given an oracle representation of its objective function: a technical note
1. Computing methodologies
  1. Artificial intelligence
    1. Planning and scheduling
2. Theory of computation
  1. Computational complexity and cryptography
    1. Problems, reductions and completeness

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cover image Computers and Operations Research

Computers and Operations Research Volume 29, Issue 14

December 2002

144 pages

ISSN:0305-0548

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Elsevier Science Ltd.

United Kingdom

Publication History

Published: 01 December 2002

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Kent CLi JBlanchet JGlynn PRanzato MBeygelzimer ADauphin YLiang PVaughan J(2021)Modified frank wolfe in probability spaceProceedings of the 35th International Conference on Neural Information Processing Systems10.5555/3540261.3541368(14448-14462)Online publication date: 6-Dec-2021
https://dl.acm.org/doi/10.5555/3540261.3541368
Wang G(2004)A novel method for parameter optimization in two-dimensional dynamical modelsProceedings of the 5th WSEAS International Conference on Applied Mathematics10.5555/1378446.1378484(1-9)Online publication date: 21-Apr-2004
https://dl.acm.org/doi/10.5555/1378446.1378484

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