zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A modified SQP method with nonmonotone technique and its global convergence. (English) Zbl 1165.90684
Summary: We propose a modified SQP method, which uses neither a penalty function nor a filter, for the nonlinear programming problems. The proposed mechanism for accepting the trial step is carried out by a nonmonotone technique. Under some conditions, we establish the global convergence of the algorithm. Some numerical results are presented to show the effectiveness of the proposed algorithm.
MSC:
90C55Methods of successive quadratic programming type
90C30Nonlinear programming
References:
[1]Han, S. P.: A global convergent method for nonlinear programing, J. optim. Theory appl. 22, 297-309 (1977)
[2]Liu, X. W.: Global convergence on an active set SQP for inequality constrained optimization, J. comput. Appl. math. 180, 201-211 (2005) · Zbl 1074.65067 · doi:10.1016/j.cam.2004.10.012
[3]Powell, M. J. D.: A fast algorithm for nonlinear constrained optimization calculations, Proceedings of the 1977 dundee biennial conference on numerical analysis, 144-157 (1978) · Zbl 0374.65032
[4]Powell, M. J. D.: The convergence of variable metric methods for nonlinear constrained optimization calculations, Nonlinear programming, vol. 3 3, 27-63 (1978) · Zbl 0464.65042
[5]J. Store, Principles of sequential quadratic programming methods for solving nonlinear programs, in: K. Schittkowski (Ed.), NATO ASI Series, vol. F15, Computational Mathematical Programming, Springer, Berlin
[6]Fletcher, R.; Leyffer, S.: Nonlinear programming without a penalty function, Math. program. 91, No. 2, 239-269 (2002) · Zbl 1049.90088 · doi:10.1007/s101070100244
[7]Chin, C. M.; Fletcher, R.: On the global convergence of an SLP-filter algorithm takes EQP steps, Math. program. 96, 161-177 (2003) · Zbl 1023.90060 · doi:10.1007/s10107-003-0378-6
[8]Fletcher, R.; Leyffer, S.; Toint, P. L.: On the global convergence of a filter-SQP algorithm, SIAM J. Optim. 13, 44-59 (2002) · Zbl 1029.65063 · doi:10.1137/S105262340038081X
[9]Fletcher, R.; Gould, N. I. M.; Leyffer, S.; Toint, P. L.; Wachter, A.: A global convergence of a trust region SQP-filter algorithm for general nonlinear programming, SIAM J. Optim. 13, 635-660 (2002) · Zbl 1038.90076 · doi:10.1137/S1052623499357258
[10]R. Fletcher, S. Leyffer, A bundle filter method for nonsmooth nonlinear optimization, Technical Report NA/195, Department of Mathematics, University of Dundee, Scotland, December, 1999
[11]Audet, C.; Dennis, J. E.: A pattern search filter method for nonlinear programming without derivatives, SIAM J. Control optim. 14, 980-1010 (2004) · Zbl 1073.90066 · doi:10.1137/S105262340138983X
[12]Long, J.; Ma, C. F.; Nie, P. Y.: A new filter method for solving nonlinear complementarity problems, Appl. math. Comput. 185, 705-718 (2007) · Zbl 1113.65062 · doi:10.1016/j.amc.2006.07.078
[13]Grippo, L.; Lampariello, F.; Ludidi, 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
[14]Bonnans, J. F.; Panier, E.; Tits, A.; Zhou, J. L.: Avoiding the maratos effect by means of a nonmonotone line search, II: Inequality constrained problems-feasible iterates, SIAM J. Numer. anal. 29, 1187-1202 (1992) · Zbl 0763.65042 · doi:10.1137/0729072
[15]Grippo, L.; Lampariello, F.; Ludidi, S.: A truncated Newton method with nonmonotone line search for unconstrained optimization, J. optim. Theory appl. 60, 401-419 (1989) · Zbl 0632.90059 · doi:10.1007/BF00940345
[16]Grippo, L.; Lampariello, F.; Ludidi, S.: A class of nonmonotone stabilization method in unconstrained optimization, Numer. math. 59, 779-805 (1991) · Zbl 0724.90060 · doi:10.1007/BF01385810
[17]Panier, E.; Tits, A.: A avoiding the maratos effect by means of nonmonotone line search, I: General constrained problems, SIAM J. Numer. anal. 28, 1183-1195 (1991) · Zbl 0732.65055 · doi:10.1137/0728063
[18]Sun, W. Y.; Han, J.; Sun, J.: Global convergence of nonmonotone descent methods for unconstrained optimization problems, J. comput. Appl. math. 146, 89-98 (2002) · Zbl 1007.65044 · doi:10.1016/S0377-0427(02)00420-X
[19]Toint, P. L.: An assessment of nonmonotone line search technique for unconstrained optimization, SIAM J. Sci. comput. 17, 725-739 (1996) · Zbl 0849.90113 · doi:10.1137/S106482759427021X
[20]Yu, Z. S.; Pu, Dingguo: A new nonmonotone line search technique for unconstrained optimization, J. comput. Appl. math. 219, 134-144 (2008) · Zbl 1149.65045 · doi:10.1016/j.cam.2007.07.008
[21]Deng, N. Y.; Xiao, Y.; Zhou, F. J.: Nonmonotone trust-region algorithm, J. optim. Theory appl. 26, 259-285 (1993) · Zbl 0797.90088 · doi:10.1007/BF00939608
[22]Fu, J. H.; Sun, W. Y.: Nonmonotone adaptive trust-region method for unconstrained optimization problems, Appl. math. Comput. 163, 489-504 (2005) · Zbl 1069.65063 · doi:10.1016/j.amc.2004.02.011
[23]Ke, X.; Han, J.: A nonmonotone trust-region algorithm for equality constrained optimization, Sci. China 38A, 683-695 (1995) · Zbl 0835.90089
[24]Ke, X.; Liu, G.; Xu, D.: A nonmonotone trust-region algorithm for unconstrained optimization, Chinese sci. Bull. 41, 197-202 (1996) · Zbl 0846.90099
[25]Sun, W. Y.: Nonmonotone trust region method for solving optimization problems, Appl. math. Comput. 156, 159-174 (2004) · Zbl 1059.65055 · doi:10.1016/j.amc.2003.07.008
[26]Toint, P. L.: A nonmonotone trust region algorithm for nonlinear optimization subject to convex constraints, Math. program. 77, 69-94 (1997) · Zbl 0891.90153
[27]Burke, J. V.; Han, S. P.: A robust SQP method, Math. program. 43, 277-303 (1989)
[28]Liu, X. W.; Yuan, Y. X.: A robust algorithm for optimization with general equality and inequality constrains, SIAM J. Sci. comput. 22, No. 2, 517-534 (2002) · Zbl 0972.65038 · doi:10.1137/S1064827598334861
[29]Zhang, J. L.; Zhang, X. S.: A modified SQP method with nonmonotone line search technique, J. global. Optim. 21, 201-218 (2001) · Zbl 1068.90616 · doi:10.1023/A:1011942228555
[30]Zhou, G. L.: A modified SQP method and its global convergence, J. global optim. 11, 193-205 (1997) · Zbl 0889.90135 · doi:10.1023/A:1008255227457
[31]Zhang, J. L.; Zhang, X. S.: A robust SQP method for optimization with inequality constraints, J. comput. Math. 21, No. 2, 247-256 (2003) · Zbl 1034.65048
[32]Nie, P. Y.; Ma, C. F.: A trust region filter method for general nonlinear programming, Appl. math. Comput. 172, 1000-1017 (2006) · Zbl 1094.65060 · doi:10.1016/j.amc.2005.03.004
[33]Hock, W.; Schittkowski, K.: Test examples for nonlinear programming codes, Lecture notes in econom. And math. Systems 187 (1981) · Zbl 0452.90038