## Convergence Properties of Optimization Algorithms for the Satisfiability (SAT) Problem (1996)

Venue: | IEEE Trans. on Computers |

Citations: | 2 - 1 self |

### BibTeX

@ARTICLE{Gu96convergenceproperties,

author = {Jun Gu and Qian-ping Gu and Ding Zhu Du},

title = {Convergence Properties of Optimization Algorithms for the Satisfiability (SAT) Problem},

journal = {IEEE Trans. on Computers},

year = {1996},

volume = {45},

pages = {209--219}

}

### OpenURL

### Abstract

: The satisfiability (SAT) problem is a basic problem in computing theory. Presently, an active area of research on SAT problem is to design efficient optimization algorithms for finding a solution for a satisfiable CNF formula. A new formulation, the Universal SAT problem model, which transforms the SAT problem on Boolean space into an optimization problem on real space has been developed [31, 35, 34, 32]. Many optimization techniques, such as the steepest descent method, Newton's method, and the coordinate descent method, can be used to solve the Universal SAT problem. In this paper, we prove that, when the initial solution is sufficiently close to the optimal solution, the steepest descent method has a linear convergence ratio fi ! 1, Newton's method has a convergence ratio of order two, and the convergence ratio of the steepest descent method is approximately (1 \Gamma fi=m) for the Universal SAT problem with m variables. An algorithm based on the coordinate descent method for the...