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GNCCP—Graduated NonConvexityand Concavity Procedure
June 2014 (vol. 36 no. 6)
pp. 1258-1267
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.
Index Terms:
Algorithm design and analysis,Linear programming,Pattern matching,NP-hard problem,Simulated annealing,Eigenvalues and eigenfunctions,quadratic assignment problem,Combinatorial optimization,graduated optimization,deterministic annealing,partial graph matching
"GNCCP—Graduated NonConvexityand Concavity Procedure," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 36, no. 6, pp. 1258-1267, June 2014, doi:10.1109/TPAMI.2013.223
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