Displaying similar documents to “A Note On M. Prešić's Method”

A new diagonal quasi-Newton algorithm for unconstrained optimization problems

Mahsa Nosrati, Keyvan Amini (2024)

Applications of Mathematics

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We present a new diagonal quasi-Newton method for solving unconstrained optimization problems based on the weak secant equation. To control the diagonal elements, the new method uses new criteria to generate the Hessian approximation. We establish the global convergence of the proposed method with the Armijo line search. Numerical results on a collection of standard test problems demonstrate the superiority of the proposed method over several existing diagonal methods.

Newton methods for solving two classes of nonsmooth equations

Yan Gao (2001)

Applications of Mathematics

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The paper is devoted to two systems of nonsmooth equations. One is the system of equations of max-type functions and the other is the system of equations of smooth compositions of max-type functions. The Newton and approximate Newton methods for these two systems are proposed. The Q-superlinear convergence of the Newton methods and the Q-linear convergence of the approximate Newton methods are established. The present methods can be more easily implemented than the previous ones, since...