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Global and local convergence of a nonmonotone trust region algorithm for equality constrained optimization. (English) Zbl 1186.90112
Summary: This paper presents a nonmonotone trust region algorithm for equality constrained optimization problems. Under certain conditions, we obtain not only the global convergence in the sense that every limit point is a stationary point but also the one step superlinear convergence rate. Numerical tests are also given to show the efficiency of the proposed algorithm.
MSC:
90C30Nonlinear programming
References:
[1]Bothina, E. S.: A global convergence theory for an active-trust-region algorithm for solving the general nonlinear programming problem, Appl. math. Comput. 144, 127-157 (2003) · Zbl 1110.65049 · doi:10.1016/S0096-3003(02)00397-1
[2]Byrd, R. H.; Schnab, R. B.; Schultz, G. A.: A trust region algorithm for nonlinearly constrained optimization, SIAM J. Numer. anal. 24, 1152-1169 (1987) · Zbl 0631.65068 · doi:10.1137/0724076
[3]A.R. Conn, N.I.M. Gould, P.L. Toint, Trust Region Methods, MSP-SIAM Series on Optimization, Philadelphia, PA, 2000.
[4]Dennis, J. E.; El-Alem, M. M.; Maciel, M. C.: A global convergence theory for general trust region-based algorithms for equality constrained optimization, SIAM J. Optimiz. 7, 177-207 (1997) · Zbl 0867.65031 · doi:10.1137/S1052623492238881
[5]Dennis, J. E.; Vicente, L. N.: On the convergence theory of trust-region-based algorithms for equality constrained optimization, SIAM J. Optimiz. 7, 927-950 (1997) · Zbl 0891.65073 · doi:10.1137/S1052623494276026
[6]X. Ke, Trust region methods for nonlinear programming, Ph.D Dissertation, Institute of Applied Mathematics, CAS, 1993.
[7]Powell, M. J. D.: On global convergence of trust region algorithms for unconstrained optimization, Math. prog. 29, 297-303 (1984) · Zbl 0569.90069 · doi:10.1007/BF02591998
[8]Powell, M. J. D.; Yuan, Y.: A trust region algorithm for equality constrained optimization, Math. prog. 49, 189-211 (1991) · Zbl 0816.90121 · doi:10.1007/BF01588787
[9]Vardi, A.: A trust region algorithm for equality constrained minimization: convergence properties and implemention, SIAM J. Numer. anal. 22, 575-591 (1985) · Zbl 0581.65045 · doi:10.1137/0722035
[10]J.L. Zhang, Trust Region Algorithm for Nonlinear Optimization, Ph.D Thesis, Institute of Applied Mathematics, Chinese Academic of Science, 2001.
[11]Zhang, J. Z.; Zhu, D. T.: A projective quasi-Newton method for nonlinear optimization, J. comput. Appl. math. 53, 291-307 (1994) · Zbl 0828.65066 · doi:10.1016/0377-0427(94)90058-2
[12]Grippo, L.; Lampariello, F.; Lucidi, S.: A nonmonotone line search technique for Newton’s method, SIAM J. Numer. anal. 23, 707-716 (1986) · Zbl 0616.65067 · doi:10.1137/0723046
[13]Chen, Z. W.; Zhang, X. S.: A nonmonotone trust region algorithm with nonmonotone penalty parameter for constrained optimization, J. comput. Appl. math. 172, 7-39 (2004) · Zbl 1059.65053 · doi:10.1016/j.cam.2003.12.048
[14]Deng, N. Y.; Xiao, Y.; Zhou, F.: Nonmonotone trust region algorithm, J. optimiz. Theory appl. 76, 259-285 (1993) · Zbl 0797.90088 · doi:10.1007/BF00939608
[15]Toint, Ph.L.: A nonmonotone trust region algorithm for nonlinear programming subject to convex constraints, Math. prog. 77, 69-94 (1997) · Zbl 0891.90153
[16]Tong, X. J.; Zhou, S. Z.: Global convergence of nonmonotone trust region algorithm for nonlinear optimization, Appl. math.: J. Chinese univ. 15, 201-210 (2000) · Zbl 1028.90065 · doi:10.1007/s11766-000-0027-2
[17]Ulbrich, M.: Nonmonotone trust region methods for bound-constrained semi-smooth equation with application to nonlinear complementarity problems, SIAM j.optim. 11, 889-917 (2001) · Zbl 1010.90085 · doi:10.1137/S1052623499356344
[18]Xu, D. C.; Han, J. Y.; Chen, Z. W.: Nonmonotone trust region method for nonlinear programming with general constraints and simple bounds, J. optimiz. Theory appl. 122, 185-206 (2004) · Zbl 1129.90353 · doi:10.1023/B:JOTA.0000041735.67285.46
[19]Zhu, D. T.: A nonmonotonic trust region technique for nonlinear constrained optimization, J. comput. Math. 13, 20-31 (1995) · Zbl 0822.65039
[20]Gould, N.; Toint, Ph.L.: Global convergence of a non-monotone trust-region filter algorithm for nonlinear programming, Proceedings of the 2004 Gainesville conference on multilevel optimization, 129-154 (2005)
[21]Su, K.; Pu, D. G.: A nonmonotone filter trust region method for nonlinear constrained optimization, J. comput. Appl. math. 223, 230-239 (2009) · Zbl 1180.65081 · doi:10.1016/j.cam.2008.01.013
[22]Ulbrich, M.; Ulbrich, S.: Non-monotone trust region methods for nonlinear equality constrained optimization without a penalty function, Math. prog. 95, 103-135 (2003) · Zbl 1030.90123 · doi:10.1007/s10107-002-0343-9
[23]W. Hock, K. Schittkowski, Test examples for nonlinear programming codes, in: Lecture Notes in Economics and Mathematics System, vol. 187, Springer-Verlag.
[24]Yuan, Y. X.; Sun, W. Y.: Optimization theory and methods, (1997)