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 nonmonotone filter trust region method for nonlinear constrained optimization. (English) Zbl 1180.65081
The following minimization problem is considered: $$\text{Minimize }f(x)\text{ subject to }c_i(x)=0\text{ for }i\in\{1,\dots,m\},$$ where $x\in \bbfR^n$, $f:\bbfR^n\to R$, and $c_i(x)$, $i\in\{1,\dots,m\}$ are twice continuously differentiable functions. The non-monotone filter technique and the fraction of Cauchy decrease are introduced. Using these concepts, the authors propose a non-monotone filter trust region algorithm for solving the minimization problem. Convergence properties and some numerical results in the concluding part of the paper show the efficiency of the proposed algorithm.

MSC:
65K05Mathematical programming (numerical methods)
Software:
ipfilter
WorldCat.org
Full Text: DOI
References:
[1] R.H. Byrd, Robust trust region methods for constrained optimization, in: Third SIAM Conference on Optimization, Houston, Texas, May, 1987
[2] Byrd, R. H.; Schnabel, R. B.; Shulta, G. A.: A trust region algorithm for nonlinear constrained optimization, SIAM J. Numer. anal. 24, 1152-1170 (1987) · Zbl 0631.65068 · doi:10.1137/0724076
[3] Celis, M. R.; Dennis, J. E.; Tapia, R. A.: A trust region strategy for nonlinear equality constrained optimization, Numerical optimization 1984 (1985) · Zbl 0566.65048
[4] Chen, Z. W.: A penalty-free-type nonmonotone trust region method for nonlinear constrained optimization, Appl. math. Comput. 173, 1014-1046 (2006) · Zbl 1093.65058 · doi:10.1016/j.amc.2005.04.031
[5] Chen, Z. W.; Zhang, X. S.: A nonmonotone trust region algorithm with nonmonotone penalty parameters for constrained optimization, J. comput. Appl. math. 172, 7-39 (2004) · Zbl 1059.65053 · doi:10.1016/j.cam.2003.12.048
[6] 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
[7] Dennis, J. E.; Ei-Alem, M.; Maciel, M. C.: A global convergence theory for general trust region based algorithms for equality constrained optimization, SIAM J. Optim. 7, 177-207 (1997) · Zbl 0867.65031 · doi:10.1137/S1052623492238881
[8] 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
[9] 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
[10] 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
[11] 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
[12] Hock, W.; Schittkowski, K.: Test examples for nonlinear programming codes, Lecture notes in economics and mathematics system 187 (1981) · Zbl 0452.90038
[13] Gomes, F. A. M.; Maciel, M. C.; Martinez, J. M.: Nonlinear programming algorithms using trust regions and augmented Lagrangian with nonmonotone penalty parameters, Math. program. 84, 161-200 (1999) · Zbl 1050.90574 · doi:10.1007/s10107980014a
[14] 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
[15] E.O. Omojokun, Trust region algorithms for optimization with nonlinear equality and inequality constraints, Ph.D. Thesis, University of Colorado, Boulder Colorado, USA, 1989
[16] Powell, M. J. D.; Yuan, Y.: A trust region algorithm for equality constrained optimization, Math. program. 49, 189-211 (1991) · Zbl 0816.90121 · doi:10.1007/BF01588787
[17] Powell, M. J. D.: Convergence properties of a class of minimization algorithm, Nonlinear programming 2, 1-27 (1975) · Zbl 0321.90045
[18] Schittkowski, K.: More test examples for nonlinear mathematical programming codes, Lecture notes in economics and mathematics system 282 (1987) · Zbl 0658.90060
[19] Ulbrich, M.; Ulbrich, S.; Vicente, L. N.: A global convergent primal-dual interior-point method for nonconvex nonlinear programming, Math. program. 100, 379-410 (2004) · Zbl 1070.90110 · doi:10.1007/s10107-003-0477-4
[20] Ulbrich, M.; Ulbrich, S.: Nonmonotone trust region methods for nonlinear equality constrianed optimization without a penalty function, Math. program. Ser. B 95, 103-135 (2003) · Zbl 1030.90123 · doi:10.1007/s10107-002-0343-9
[21] Ulbrich, S.: On the superlinear local convergence of a filter-SQP method, Math. program. 100, 217-245 (2004) · Zbl 1146.90525 · doi:10.1007/s10107-003-0491-6