On optimizing the satisfiability (SAT) problem
Authors: 
Jun Gu, Qianping Gu, Dingzhu DuAuthors Info & Claims
Jun Gu, Qianping Gu, Dingzhu DuAuthors Info & ClaimsPages 1 - 17
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 satisfiableCNF formula. A new formulation, theUniversal SAT problem model, which transforms the SAT problem on Boolean space into an optimization problem on real space has been developed. Many optimization techniques, such as the steepest descent method, Newton's method, and the coordinate descent method, can be used to solve theUniversal 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 β<1, Newton's method has a convergence ratio of order tow, and the convergence ratio of the coordinate descent method is approximately (1-β/m) for theUniversal SAT problem withm variables. An algorithm based on the coordinate descent method for theUniversal SAT problem is also presented in this paper.
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© Science Press, Beijing China and Allerton Press Inc. 1999.
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Publication History
Published: 01 January 1999
Received: 08 October 1998
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