, Volume 10, Issue 3, pp 302-314

A branch bound method for subset sum problem

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Abstract

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.

The whole paper was completed while the author was studying in the laboratoire d'économétrie de l'Ecole Polytechnique, Paris, France.