Convergence of the nonmonotone Perry and Shanno method for optimization

Computational Optimization and Applications

Volumn 16, Issue 2, 2000, Pages 159-172

  Liu, Guanghui ^a   Jing, Lili ^b  

^a Northwestern University   (United States)

^b BEIJING FORESTRY UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; FUNCTIONS; INVERSE PROBLEMS; ITERATIVE METHODS; PROBLEM SOLVING; THEOREM PROVING;

CONJUGATE GRADIENT METHOD; CONVEX OBJECTIVE FUNCTIONS; GLOBAL CONVERGENCE; NONMONOTONE PERRY METHOD; NONMONOTONE SHANNO METHOD; QUASI NEWTON METHOD;

OPTIMIZATION;

EID: 0034226290     PISSN: 09266003     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008753308646     Document Type: Article

References (27)

1. E.M.L. Beale, "On an iterative method of finding a local minimum of a function of more than one variable," Technical Report No. 25, Statistical Techniques Research Group, Princeton University, N.J., 1958.
2. I. Bongartz, A.R. Conn, N. Gould, and Ph.L. Toint, "CUTE: constrained and unconstrained testing environment," Research Report, IBM T.J. Watson Research Center, Yorktown Heights, NY, 1993.
3. K.M. Brown and J.E. Dennis Jr., "New computational algorithms for minimizing a sum of squares of nonlinear functions," Report No. 71-6, Department of Computer Science, Yale University, New Haven, Connecticut, U.S.A., March 1971.
4. A. Buckley, "A combined conjugate gradient quasi-newton minimization algorithm," Mathematical Programming, vol. 15, pp. 200-210, 1978.
5. A. Buckley and A. LeNir, "QN-like variable storage conjugate gradients," Mathematical Programming, vol. 27, pp. 155-175, 1983.
6. R.H. Byrd and J. Nocedal, "A tool for the analysis of quasi-newton methods with application to unconstrained minimization," SIAM J. Numer. Anal., vol. 26, pp. 727-739, 1989.
7. R.H. Byrd, J. Nocedal, and R.B. Schnabel, "Representations of quasi-newton matrices and their use in limited memory methods," Mathematical Programming, vol. 63, pp. 129-156, 1994.
8. R.H. Byrd, J. Nocedal, and Y. Yuan, "Global convergence of a class of quasi-newton methods on convex problems," SIAM J. Numer. Anal., vol. 24, pp. 1171-1189, 1987.
9. P.E. Gill and W. Murray, "The numerical solution of a problem in the calculus of variations," in Recent Mathematical Developments in Control, D.J. Bell (Ed.), Academic Press: New York, 1973, pp. 97-122.
10. P.E. Gill and W. Murray, "Conjugate gradients for large-scale nonlinear optimization," Technical Report SOL n79-15, Department of Operations Research, Stanford University, Stanford, CA, 1979.
11. L. Grippo, F. Lampariello, and S. Lucidi, "A nonmonotone linesearch technique for newton's methods," SIAM J. Numer. Anal., vol. 23, pp. 707-716, 1986.
12. J.Y. Han and G.H. Liu, "General form of stepsize selection rule of linesearch and relevant analysis of global convergence of BEGS algorithm," Acta Mathematicae Applicatae Sinica, vol. 8, no. 1, pp. 112-122, 1992.
13. D.C. Liu and J. Nocedal, "Test results of two limited memory methods for large scale optimization," Technical Report NAM 04, Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, 1988.
14. D.C. Liu and J. Nocedal, "On the limited memory BEGS method for large scale optimization," Mathematical Programming, vol. 45, pp. 503-528, 1989.
15. G.H. Liu, J.Y. Han, and D.F. Sun, "Global convergence of the BEGS algorithm with nonmonotone linesearch," Optimization, vol. 34, pp. 147-159, 1995.
16. G.H. Liu, L.L. Jing, L.X. Han, and D. Han, "A class of nonmonotone conjugate gradient methods for unconstrained optimization," Journal of Optimization Theory and Applications, vol. 101, no. 1, 1999.
17. S. Lucidi and M. Roma, "Nonmonotone conjugate gradient methods for optimization," in System Modelling and Optimization, J. Henry and J.D. Yvon (Eds.), Sringer Verlag, 1995. Lecture Notes on Control and Information Sciences.
18. J.J. More, B.S. Garbow, and K.E. Hillstrom, "Testing unconstrained optimization software," ACM Transactions on Mathematical Software, vol. 7, no. 1, pp. 17-41, 1980.
19. L. Nazareth, "A relationship between the BEGS and conjugate gradient algorithms and its implications for new algorithms," SIAM Journal on Numerical Analysis, vol. 16, pp. 794-800, 1979.
20. J. Nocedal, "Updating quasi-newton matrices with limited storage," Mathematics of Computation, vol. 35, pp. 773-782, 1980.
21. M.J.D. Powell, "Some global convergence properties of a variable metric algorithm for minimization without exact linesearches," in Nonlinear Programming, SIAM-AMS Proceedings, Vol. IX., R.W. Cottle and C.E. Lemke (Eds.), American Mathematical Society, Providence, RI, 1976.
22. J.M. Perry, "A class of conjugate gradient algorithms with a two step variable metric memory," Discussion Paper 269, Center for Mathematical Studies in Economicas and Management Science, Northwestern University, Evanston, IL, 1977.
23. D.F. Shanno, "On the convergence of a new conjugate gradient algorithm," SIAM Journal on Numerical Analysis, vol. 15, pp. 1247-1257, 1978.
24. D.F. Shanno, "Conjugate gradient methods with inexact searches," Mathematics of Operations Research, vol. 3, pp. 244-256, 1978.
25. F.F. Sisser, "A modified Newton's method for minimizing factorable functions," Manuscript, Queens College of The City University of New York, Flushing, N.Y, U.S.A., 1980.
26. Ph.L. Toint, "Test problems for partially separable optimization and results for the routine PSPMIN," Technical Report Rpt. 83/4, Facultes University de Namur, Department of Mathematics, B-5000, Namur, Belgium, 1983.
27. J. Werner, "Global convergence of quasi-newton methods with practical linesearches," Technical Report, NAM-Bericht Nr.67, Marz, 1989.