On complexity of unconstrained hyperbolic 0-1 programming problems

Authors:
Oleg A. Prokopyev;Hong-Xuan Huang;Panos M. Pardalos
Affiliations:
Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL 32611, USA;Department of Mathematical Sciences, Tsinghua University, Beijing 100084, PR China;Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL 32611, USA
Venue:
Operations Research Letters
Year:
2005

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Abstract

Single- and multiple-ratio unconstrained hyperbolic 0-1 programming problems are considered. We prove that checking whether these problems have a unique solution is NP-hard. Furthermore, we show that finding the global maximizer of problems with unique solution remains NP-hard. We also discuss complexity of local search and approximability for multiple-ratio problems.