Positive Definiteness of Symmetric Rank 1 (H-Version) Update for Unconstrained Optimization

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Saad Shakir Mahmood
Jaafer Hmood Eidi
Jinan Adel Jasem

Abstract

Several attempts have been made to modify the quasi-Newton condition in order to obtain rapid convergence with complete properties (symmetric and positive definite) of the inverse of  Hessian matrix (second derivative of the objective function). There are many unconstrained optimization methods that do not generate positive definiteness of the inverse of Hessian matrix. One of those methods is the symmetric rank 1( H-version) update (SR1 update), where this update satisfies the quasi-Newton condition and the symmetric property of inverse of Hessian matrix, but does not preserve the positive definite property of the inverse of Hessian matrix where the initial inverse of Hessian matrix is positive definiteness. The positive definite property for the inverse of Hessian matrix is very important to guarantee the existence of the minimum point of the objective function and determine the minimum value of the objective function.

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1.
Mahmood SS, Eidi JH, Jasem JA. Positive Definiteness of Symmetric Rank 1 (H-Version) Update for Unconstrained Optimization. Baghdad Sci.J [Internet]. [cited 2021Dec.4];19(2):0297. Available from: https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/5144
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