Globally convergent algorithms for solving unconstrained optimization problems
- Authors: Taheri, Sona , Mammadov, Musa , Seifollahi, Sattar
- Date: 2013
- Type: Text , Journal article
- Relation: Optimization Vol. , no. (2013), p. 1-15
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- Description: New algorithms for solving unconstrained optimization problems are presented based on the idea of combining two types of descent directions: the direction of anti-gradient and either the Newton or quasi-Newton directions. The use of latter directions allows one to improve the convergence rate. Global and superlinear convergence properties of these algorithms are established. Numerical experiments using some unconstrained test problems are reported. Also, the proposed algorithms are compared with some existing similar methods using results of experiments. This comparison demonstrates the efficiency of the proposed combined methods.
A new method for solving linear ill-posed problems
- Authors: Zhang, Jianjun , Mammadov, Musa
- Date: 2012
- Type: Text , Journal article
- Relation: Applied Mathematics and Computation Vol. 218, no. 20 (2012), p.10180-10187
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- Description: In this paper, we propose a new method for solving large-scale ill-posed problems. This method is based on the Karush-Kuhn-Tucker conditions, Fisher-Burmeister function and the discrepancy principle. The main difference from the majority of existing methods for solving ill-posed problems is that, we do not need to choose a regularization parameter in advance. Experimental results show that the proposed method is effective and promising for many practical problems. © 2012.