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    An exact penalty method for binary optimization based on MPEC formulation

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    Type
    Conference Paper
    Authors
    Yuan, Ganzhao
    Ghanem, Bernard cc
    KAUST Department
    Visual Computing Center (VCC)
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Electrical Engineering Program
    Date
    2017-01-01
    Permanent link to this record
    http://hdl.handle.net/10754/666700
    
    Metadata
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    Abstract
    Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques, which is based on Mathematical Programming with Equilibrium Constraints (MPECs). We first reformulate the binary program as an equivalent augmented biconvex optimization problem with a bilinear equality constraint, then we propose an exact penalty method to solve it. The resulting algorithm seeks a desirable solution to the original problem via solving a sequence of linear programming convex relaxation subproblems. In addition, we prove that the penalty function, induced by adding the complementarity constraint to the objective, is exact, i.e., it has the same local and global minima with those of the original binary program when the penalty parameter is over some threshold. The convergence of the algorithm can be guaranteed, since it essentially reduces to block coordinate descent in the literature. Finally, we demonstrate the effectiveness of our method on the problem of dense subgraph discovery. Extensive experiments show that our method outperforms existing techniques, such as iterative hard thresholding and linear programming relaxation.
    Sponsors
    This work was supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research through the Visual Computing Center (VCC) funding. Yuan is also supported by NSF-China (61402182). A special thanks is also extended to Prof. Shaohua Pan and Dr. Li Shen (South China University of Technology) for their helpful discussions on this paper.
    Publisher
    AAAI press
    Conference/Event name
    31st AAAI Conference on Artificial Intelligence, AAAI 2017
    Additional Links
    https://research.kaust.edu.sa/en/publications/an-exact-penalty-method-for-binary-optimization-based-on-mpec-for
    Collections
    Conference Papers; Electrical and Computer Engineering Program; Visual Computing Center (VCC); Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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