Abstract
In this paper, a generalized projection quasi‐Newton method with inexact line search is proposed for the nonlinear optimization problem with linear constraints. The projection andquasi‐Newton technique are used to determine the search direction at each iteration. It is proved that the method has properties of global convergence and superlinear convergence rate under some suitable assumptions.
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References
D. Goldfarb, Extension of Davidon's variable metric method to maximization under linear inequality and equality constraints, SIAM. J. Appl. Math. 17(1969)739-364.
D.Z. Du and J. Sun, A new gradient projection method, Math. Numer. Sinica 6(1984)378-376.
F. Wu, A superlinear convergent gradient projection type algorithm for linearly constrained problem, Eur. J. of Oper. Res. 16(1984) 334-334.
X. Gui and D. Du, A superlinear convergent method to linearly constrained optimization under degeneracy, Acta. Math. Appl. Sinica 1(1984)76-84.
Y.L. Lai, F. Wu and H.Y. Kwi, Reduced variable metric method for linearly constrained convex programming, Science in China (series A) 26(1983)785-794.
Z.Y. Gao and G.P. He, A generalized gradient projection algorithm for constrained optimization problem, Chinese Science Bulletin 36(1991)1444-1447.
Y.L. Lai, Z.Y. Gao and G.P. He, A generalized gradient projection algorithm of optimization with nonlinear constraints, Science in China (series A) 36((1993)170-180.
}Z.Y. Gao, Feasible methods for nonlinear programming with nonlinear constraints and their convergent properties, Ph.D. Thesis, Institute of Applied Mathematics, Academia Sinica, Beijing, China, 1993.
G.P. He, Some new superlinearly convergent algorithms for nonlinear programming problems, Ph.D. Thesis, Institute of Applied Mathematics, Academia Sinica, Beijing, China, 1995.
R. Fletcher, Practical Methods of Optimization, Vol. 2, 1981.
M.J.D. Powell, Some global convergence properties of a variable metric algorithm for minimization without exact linear searches, SIAM-AMS Proceedings 9, 1976.
W. Hock and K. Schittkowski, Test Examples for Nonlinear Programming Codes, Lecture Notes in Economics and Mathematical Systems 187, Springer, Berlin, 1981.
P. Wolfe, Methods of nonlinear programming, in: Nonlinear Programming, ed. J. Abadie, Wiley Interscience, New York, 1967, pp. 97-131.
K. Schittkowski, More Test Examples for Nonlinear Programming Codes, Lecture Notes in Economics and Mathematical Systems 282, Springer, Berlin, 1987.
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Lai, Y., Gao, Z. & He, G. A generalized projection quasi‐Newton method for nonlinear optimization problems. Annals of Operations Research 87, 353–362 (1999). https://doi.org/10.1023/A:1018949406680
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DOI: https://doi.org/10.1023/A:1018949406680