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 ...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 Boofean 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 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 β<1, Newton's method has a convergence ratio of order two, and the convergence ratio of the coordinate descent method is approximately (1-β/m) for the Universal SAT problem with m variables. An algorithm based on the coordinate descent method for the Universal SAT problem is also presented in this paper.展开更多
基金NSERC Strategic Grant MEF0045793NSERC Research Grant OGP0046423.
文摘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 Boofean 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 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 β<1, Newton's method has a convergence ratio of order two, and the convergence ratio of the coordinate descent method is approximately (1-β/m) for the Universal SAT problem with m variables. An algorithm based on the coordinate descent method for the Universal SAT problem is also presented in this paper.
