Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 617398, 18 pages
Research Article

Reverse Bridge Theorem under Constraint Partition

1College of Computer, Northeast Normal University, Changchun 130117, China
2Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University, Changchun 130012, China

Received 6 October 2009; Revised 7 January 2010; Accepted 7 May 2010

Academic Editor: Joaquim J. Júdice

Copyright © 2010 Minghao Yin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Reverse bridge theorem (RBTH) has been proved to be both a necessary and sufficient condition for solving Nonlinear programming problems. In this paper, we first propose three algorithms for finding constraint minimum points of continuous, discrete, and mixed-integer nonlinear programming problems based on the reverse bridge theorem. Moreover, we prove that RBTH under constraint partition is also a necessary and sufficient condition for solving nonlinear programming problems. This property can help us to develop an algorithm using RBTH under constraints. Specifically, the algorithm first partitions mixed-integer nonlinear programming problems (MINLPs) by their constraints into some subproblems in similar forms, then solves each subproblem by using RBTH directly, and finally resolves those unsatisfied global constraints by choosing appropriate penalties. Finally, we prove the soundness and completeness of our algorithm. Experimental results also show that our algorithm is effective and sound.