| dc.contributor.author | Mahmood, Saad Shakir | |
| dc.date.accessioned | 2012-12-18T10:01:27Z | |
| dc.date.available | 2012-12-18T10:01:27Z | |
| dc.date.issued | 2012-01 | |
| dc.identifier.citation | Byrd R. H. and Nocedal J. 1989. A tool for the analysis of quasi-Newton methods with application to unconstrained minimization. SIAM J. Number. Anal., 26: 727-739 Bartle R. G. 1975. The elements of real analysis. Wiley international edition. USA. 286-330 David G. Luenberger and Yinyu Ye. 2009. linear and Nonlinear Programming. Third Edition. Springer Dennis J. E. and Schnabel R. B. 1983. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall, Inc., Englewood Cliffs, New Jersey. Hart, W. E. 1990. Quasi-Newton methods for sparse Nonlinear system. Memorandum CSM-151, Department of Computer Science, University of Essex. Royden, H. L. 1968. Real Analysis. second edition, Macmillan Publishing co. INC. New York. Saad S.. 2003. Unconstrained Optimization Methods Based On Direct Updating of Hessian Factors. Ph. D. Dissertation. Gadjah Mada University. Yogyakarta, Indonesia. Steven C. Chapra. 2005."Applied Numerical Methods With MATLAB for Engineers and Scientists. McGRAW- HILL INTERNATIONAL EDITION. | en_US |
| dc.identifier.issn | 20087-085X | |
| dc.identifier.uri | http://hdl.handle.net/11617/2381 | |
| dc.description.abstract | It is well known that the unconstrained Optimization often arises in economies, finance,
trade, law, meteorology, medicine, biology, chemistry, engineering, physics, education, history,
sociology, psychology, and so on. The classical Unconstrained Optimization is based on the
Updating of Hessian matrix and computed of its inverse which make the solution is very
expensive. In this work we will updating the LU factors of the Hessian matrix so we don’t need to
compute the inverse of Hessian matrix, so called the Cholesky Update for unconstrained
optimization. We introduce the convergent of the update and report our findings on several
standard problems, and make a comparison on its performance with the well-accepted BFGS
update. | en_US |
| dc.publisher | LPPM UMS | en_US |
| dc.subject | Unconstrained Optimization | en_US |
| dc.subject | Cholesky Factorization | en_US |
| dc.subject | Convergence | en_US |
| dc.title | THE CHOLESKY UPDATE FOR UNCONSTRAINED OPTIMIZATION | en_US |
| dc.type | Article | en_US |
