New Hybrid Globally Convergent CG-Algorithms for Nonlinear Unconstrained Optimization

Problem Statement: Conjugate gradient methods, which we have investigated in this study, were widely used in optimization, especially for large scale optimization problems, because it does not need the storage of any matrix. The purpose of this construction is to find new CG-algorithms suitable for solving large scale optimization problems with obtaining better numerical results. Approach: In this study, we made three linear combinations for the proposed family of CG-methods, the first resulted from the linear combination of Andrei 2007 and Powell 1984 methods; the second yielded from Andrei 2007 and Dai-Liao 2001 methods while the third was a combination of Andrei 2007 and Yabe-Takano 2003 methods. Results: Numerical results, showed that the presented new CG-algorithms have been proved to be effective algorithms in solving large scale optimization problems and gave us a good numerical results. Conclusion: Our new proposed algorithms always produce descent search directions and were shown to be globally convergent under some assumptions