A New Preconditioned Inexact Line-Search Technique for Unconstrained Optimization
In this paper, we study the global convergence properties of the new class of preconditioned conjugate gradient descent algorithm, when applied to convex objective non-linear unconstrained optimization functions. We assume that a new inexact line search rule which is similar to the Armijo line-searc...
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| Veröffentlicht in: | AL-Rafidain journal of computer sciences and mathematics Jg. 9; H. 2; S. 25 - 39 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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Mosul University
04.12.2012
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| ISSN: | 1815-4816, 2311-7990 |
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| Abstract | In this paper, we study the global convergence properties of the new class of preconditioned conjugate gradient descent algorithm, when applied to convex objective non-linear unconstrained optimization functions. We assume that a new inexact line search rule which is similar to the Armijo line-search rule is used. It's an estimation formula to choose a large step-size at each iteration and use the same formula to find the direction search. A new preconditioned conjugate gradient direction search is used to replace the conjugate gradient descent direction of ZIR-algorithm. Numerical results on twenty five well-know test functions with various dimensions show that the new inexact line-search and the new preconditioned conjugate gradient search directions are efficient for solving unconstrained nonlinear optimization problem in many situations. |
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| AbstractList | In this paper, we study the global convergence properties of the new class of preconditioned conjugate gradient descent algorithm, when applied to convex objective non-linear unconstrained optimization functions. We assume that a new inexact line search rule which is similar to the Armijo line-search rule is used. It's an estimation formula to choose a large step-size at each iteration and use the same formula to find the direction search. A new preconditioned conjugate gradient direction search is used to replace the conjugate gradient descent direction of ZIR-algorithm. Numerical results on twenty five well-know test functions with various dimensions show that the new inexact line-search and the new preconditioned conjugate gradient search directions are efficient for solving unconstrained nonlinear optimization problem in many situations. |
| Author | Abbas Y. Al-Bayati Ivan S. Latif |
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| SubjectTerms | inexact line-search preconditioned cg self-scaling vm-update unconstrained optimization |
| Title | A New Preconditioned Inexact Line-Search Technique for Unconstrained Optimization |
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