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A new diagonal quasi-Newton algorithm for unconstrained optimization problems

Mahsa Nosrati;  Keyvan Amini — 2024

Applications of Mathematics

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.

A new nonmonotone adaptive trust region algorithm

Ahmad Kamandi;  Keyvan Amini — 2022

Applications of Mathematics

We propose a new and efficient nonmonotone adaptive trust region algorithm to solve unconstrained optimization problems. This algorithm incorporates two novelties: it benefits from a radius dependent shrinkage parameter for adjusting the trust region radius that avoids undesirable directions and exploits a new strategy to prevent sudden increments of objective function values in nonmonotone trust region techniques. Global convergence of this algorithm is investigated under some mild conditions....

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