Acta Mathematicae Applicatae Sinica

, Volume 10, Issue 3, pp 302-314

First online:

A branch bound method for subset sum problem

  • Wu Shiquan Affiliated withInstitute of Applied Mathematics, the Chinese Academy of Sciences

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This paper indicates the possible difficulties for applying the interior point method to NP-complete problems, transforms an NP-complete problem into a nonconvex quadratic program and then develops some convexity theories for it. Lastly it proposes an algorithm which uses Karmarkar's algorithm as a subroutine. The finite convergence of this algorithm is also proved.

Key words

Subset sum problem nonconvex quadratic program convex envelope interior point method