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Solving Trust Region Subproblems With Combination of Cauchy, Newton and Borza Vectors for Unconstrained Optimization Problems

M. Borza, F. Asgari, F. Pidani


On using a positive linear combination of Cauchy , Newton and Borza vectors,we could obtain a method for solving trust region subproblems.In this method,the linear combination has to be designed in such a way that, in each iteration , the Borza coefficient is assumed to be equal to one and then try to calculate and determine the Cauchy and Newton coefficients in the sense that the vector magnitude obtained not to exceed the radius of trust region and the reduction obtained is to be more than Borza’s and Cauchy’s reductions. We show that this method has global convergence property. a numerical Example is illustrated for comparing this method with Borza and Cauchy method.


Trust region,Rank two update,Cauchy method, Newton method, Borza method,Reduction algorithm family,Global convergence.

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