Issue No. 06 - June (2014 vol. 36)
Zhi-Yong Liu , State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Room 904, Zidonghua Building, 95 Zhongguan East Road, China
Hong Qiao , State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Room 904, Zidonghua Building, 95 Zhongguan East Road, China
In this paper we propose the graduated nonconvexity and concavity procedure (GNCCP) as a general optimization framework to approximately solve the combinatorial optimization problems defined on the set of partial permutation matrices. GNCCP comprises two sub-procedures, graduated nonconvexity which realizes a convex relaxation and graduated concavity which realizes a concave relaxation. It is proved that GNCCP realizes exactly a type of convex-concave relaxation procedure (CCRP), but with a much simpler formulation without needing convex or concave relaxation in an explicit way. Actually, GNCCP involves only the gradient of the objective function and is therefore very easy to use in practical applications. Two typical related NP-hard problems, partial graph matching and quadratic assignment problem (QAP), are employed to demonstrate its simplicity and state-of-the-art performance.
Algorithm design and analysis, Linear programming, Pattern matching, NP-hard problem, Simulated annealing, Eigenvalues and eigenfunctions
Zhi-Yong Liu, Hong Qiao, "GNCCP—Graduated NonConvexityand Concavity Procedure", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 36, no. , pp. 1258-1267, June 2014, doi:10.1109/TPAMI.2013.223