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1860796985227870208
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INTELEK Repository
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Online Access
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https://intelek.unisza.edu.my/intelek/pages/search.php?search=!collection407072
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2024-10-04 15:42
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Restricted Document
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10934
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UniSZA
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[1] N. Andrei, An unconstrained optimization test functions collection, Adv. Model. Optim. 10(2008), 147-161. [2] A. R. Conn, N. I. M. Gould, and Ph. Toint, Convergence of quasi-Newton matrices generated by the symmetric rank one update, Math. program. 48(1991), 549-560. [3] J. E. Dennis, Numerical methods for unconstrained optimization and nonlinear equations, Prince-Hall, Inc., Englewood Cliffs, New Jersey (1983). [4] J. E. Dennis and J. J. More, A characterization of superlinear convergence and its application to quasi-Newton methods, Math. Comp. 28(1974), 549- 560. [5] J. E. Dennis and H. Wolkowicz, Sizing and least change secant methods, SIAM J. Numer. Anal. 30(5)(1993), 1291-1313. [6] H. F. H. Khalfan, R. H. Byrd, and R. B. Schnabel, A theoretical and experimental study of the symmetric rank one update, SIAM J. Optim. 3(1993), 1-24 . [7] H. F. H. Khalfan, Topics in quasi-Newton methods for unconstrained optimization, Ph.D. thesis, University of Colorado, Colorado (1989). [8] W. J. Leong and M. A. Hassan, A restarting approach for the symmetric rank one update for unconstrained optimization, Comp. Optim. Appl. 42(3)(2009), 327-334. [9] W. J. Leong and M. A. Hassan, Convergence of a positive definite symmetric rank one method with restart, Adv. Model. Optim. 11(4)(2009), 423-433. [10] F. Modarres, M. A. Hassan and W. J. Leong, A symmetric rank-one method based on extra updating techniques for unconstrained optimzation, Comp. Math. Appl. 62(2011), 392-400. [11] F. Modarres, M. A. Hassan and W. J. Leong, Structured symmetric rank-one method for unconstrained optimzation, Int. J. Comp. Math. 88:12(2011), 2608-2617. [12] J. Nocedal and S. J. Wright, Numerical Optimization, Springer series in Opration Research, USA, (2006). [13] M. R. Osborne and L. Sun, A new approach to symmetric rank-one updating, IMA J. Numer. Anal. 19(1999), 497-507. [14] P. A. Spellucci, A modified rank one update which converges Qsuperlinearly, Comp. Optim. Appl. 19 (2001), 273-296. [15] H. Wolkowicz, Measures for symmetric rank-one updates, Math. Oper. Res. 19(4)(1994), 815-830.
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10934 https://intelek.unisza.edu.my/intelek/pages/view.php?ref=10934 https://intelek.unisza.edu.my/intelek/pages/search.php?search=!collection407072 Restricted Document Article Journal image/jpeg inches 96 96 628 1340 2024-10-04 15:42 1340x628 5079-01-FH02-FIK-14-00733.jpg UniSZA Private Access Scaling strategies for symmetric rank-one method in solving unconstrained optimization problems Applied Mathematical Sciences Symmetric rank-one update (SR1) is known to have good numerical performance among the quasi-Newton methods for solving unconstrained optimization problems as evident from the recent study of Farzin et al. (2011), However, it is well known that the SR1 update may not preserve positive definiteness even when updated from a positive definite approximation and can be undefined with zero denominator. In this paper, we propose some scaling strategies to overcome these well known shortcomings of the SR1 update. Numerical experiment showed that the proposed strategies are very competitive, encouraging and have exhibited a clear improvement in the numerical performance over SR1 algorithms with some existing strategies in avoiding zero denominator and preserving positive-definiteness. 8 25 1247-1260 [1] N. Andrei, An unconstrained optimization test functions collection, Adv. Model. Optim. 10(2008), 147-161. [2] A. R. Conn, N. I. M. Gould, and Ph. Toint, Convergence of quasi-Newton matrices generated by the symmetric rank one update, Math. program. 48(1991), 549-560. [3] J. E. Dennis, Numerical methods for unconstrained optimization and nonlinear equations, Prince-Hall, Inc., Englewood Cliffs, New Jersey (1983). [4] J. E. Dennis and J. J. More, A characterization of superlinear convergence and its application to quasi-Newton methods, Math. Comp. 28(1974), 549- 560. [5] J. E. Dennis and H. Wolkowicz, Sizing and least change secant methods, SIAM J. Numer. Anal. 30(5)(1993), 1291-1313. [6] H. F. H. Khalfan, R. H. Byrd, and R. B. Schnabel, A theoretical and experimental study of the symmetric rank one update, SIAM J. Optim. 3(1993), 1-24 . [7] H. F. H. Khalfan, Topics in quasi-Newton methods for unconstrained optimization, Ph.D. thesis, University of Colorado, Colorado (1989). [8] W. J. Leong and M. A. Hassan, A restarting approach for the symmetric rank one update for unconstrained optimization, Comp. Optim. Appl. 42(3)(2009), 327-334. [9] W. J. Leong and M. A. Hassan, Convergence of a positive definite symmetric rank one method with restart, Adv. Model. Optim. 11(4)(2009), 423-433. [10] F. Modarres, M. A. Hassan and W. J. Leong, A symmetric rank-one method based on extra updating techniques for unconstrained optimzation, Comp. Math. Appl. 62(2011), 392-400. [11] F. Modarres, M. A. Hassan and W. J. Leong, Structured symmetric rank-one method for unconstrained optimzation, Int. J. Comp. Math. 88:12(2011), 2608-2617. [12] J. Nocedal and S. J. Wright, Numerical Optimization, Springer series in Opration Research, USA, (2006). [13] M. R. Osborne and L. Sun, A new approach to symmetric rank-one updating, IMA J. Numer. Anal. 19(1999), 497-507. [14] P. A. Spellucci, A modified rank one update which converges Qsuperlinearly, Comp. Optim. Appl. 19 (2001), 273-296. [15] H. Wolkowicz, Measures for symmetric rank-one updates, Math. Oper. Res. 19(4)(1994), 815-830.
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| spellingShingle |
Scaling strategies for symmetric rank-one method in solving unconstrained optimization problems
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| summary |
Symmetric rank-one update (SR1) is known to have good numerical performance among the quasi-Newton methods for solving unconstrained optimization problems as evident from the recent study of Farzin et al. (2011), However, it is well known that the SR1 update may not preserve positive definiteness even when updated from a positive definite approximation and can be undefined with zero denominator. In this paper, we propose some scaling strategies to overcome these well known shortcomings of the SR1 update. Numerical experiment showed that the proposed strategies are very competitive, encouraging and have exhibited a clear improvement in the numerical performance over SR1 algorithms with some existing strategies in avoiding zero denominator and preserving positive-definiteness.
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| title |
Scaling strategies for symmetric rank-one method in solving unconstrained optimization problems
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| title_full |
Scaling strategies for symmetric rank-one method in solving unconstrained optimization problems
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| title_fullStr |
Scaling strategies for symmetric rank-one method in solving unconstrained optimization problems
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| title_full_unstemmed |
Scaling strategies for symmetric rank-one method in solving unconstrained optimization problems
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| title_short |
Scaling strategies for symmetric rank-one method in solving unconstrained optimization problems
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| title_sort |
scaling strategies for symmetric rank-one method in solving unconstrained optimization problems
|