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. Kovalyov
Affiliations:
Department of Management, The Hong Kong Polytechnic University, Hung Hom Kowloon, Hong Kong;Institute of Engineering Cybernetics, National Academy of Sciences of Belarus, Sugranova 6, 220012 Minsk, Belarus
Venue:
Computers and Operations Research
Year:
2002

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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.