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In this paper, a variable metric algorithm is proposed with Broyden rank one modifications for the equality constrained optimization. This method is viewed expansion in constrained optimization as the quasi-Newton method to unconstrained optimization. The theoretical analysis shows that local convergence can be induced under some suitable conditions. In the end, it is established an equivalent condition of superlinear convergence.doi:10.4236/ojop.2013.21005 fatcat:csmg7oajwfa5nbwyuia6wja7vy