A quasi-Newton method with Cholesky factorization |
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Authors: | Dr. J. Bräuninger |
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Affiliation: | 1. Mathematisches Institut A, Universit?t Stuttgart, Pfaffenwaldring 57, D-7000, Stuttgart 80, Federal Republic of Germany
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Abstract: | ![]() A quasi-Newton method for unconstrained minimization is presented, which uses a Cholesky factorization of an approximation to the Hessian matrix. In each step a new row and column of this approximation matrix is determined and its Cholesky factorization is updated. This reduces storage requirements and simplifies the calculation of the search direction. Precautions are taken to hold the approximation matrix positive definite. It is shown that under usual conditions the method converges superlinearly or evenn-step quadratic. |
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