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GQTPAR

swMATH ID: 7451
Software Authors: Moré, Jorge J.; Sorensen, D.C.
Description: Computing a trust region step We propose an algorithm for the problem of minimizing a quadratic function subject to an ellipsoidal constraint and show that this algorithm is guaranteed to produce a nearly optimal solution in a finite number of iterations. We also consider the use of this algorithm in a trust region Newton’s method. In particular, we prove that under reasonable assumptions the sequence generated by Newton’s method has a limit point which satisfies the first and second order necessary conditions for a minimizer of the objective function. Numerical results for GQTPAR, which is a Fortran implementation of our algorithm, show that GQTPAR is quite successful in a trust region method. In our tests a call to GQTPAR only required 1.6 iterations on the average.
Homepage: http://epubs.siam.org/doi/abs/10.1137/0904038
Keywords: Newton’s method; trust region; ellipsoidal constraint; global convergence
Related Software: HSL-VF05; CUTEr; minpack; LSTRS; LANCELOT; Matlab; L-BFGS; SifDec; GALAHAD; Regularization tools; CUTEst; ARPACK; UOBYQA; DFO; tn; NEWUOA; LAPACK; KELLEY; CUTE; MSS
Cited in: 333 Publications

Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
Computing a trust region step. Zbl 0551.65042
Moré, Jorge J.; Sorensen, D. C.
1983
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Cited by 477 Authors

14 Yuan, Ya-xiang
11 Zhu, Detong
8 Kanzow, Christian
8 Shen, Chungen
8 Zhang, Lei-Hong
7 Beck, Amir
7 Erway, Jennifer B.
7 Lukšan, Ladislav
7 Moré, Jorge J.
7 Schnabel, Robert B.
7 Wolkowicz, Henry
7 Xia, Yong
6 Coleman, Thomas F.
6 Gould, Nicholas Ian Mark
6 Li, Duan
6 Marcia, Roummel F.
6 Qi, Liqun
6 Salahi, Maziar
5 Bellavia, Stefania
5 Jiang, Rujun
5 Martínez, José Mario
5 Morini, Benedetta
5 Pham Dinh Tao
5 Xiu, Naihua
4 Abdel-Aziz, Mohammedi R.
4 Byrd, Richard H.
4 Qi, Houduo
4 Robinson, Daniel P.
4 Sun, Wenyu
4 Taati, Akram
4 Vicente, Luis Nunes
3 Ben-Tal, Aharon
3 Burer, Samuel
3 Chu, Delin
3 Chu, Moody T.
3 Curtis, Frank E.
3 Fukushima, Masao
3 Guan, Yu
3 Jian, Jinbao
3 Kılınç Karzan, Fatma
3 Larson, Jeffrey
3 Le Thi, Hoai An
3 Li, Rencang
3 Li, Yuying
3 Mai-Duy, Nam
3 Ni, Qin
3 Reichel, Lothar
3 Santos, Sandra Augusta
3 Sorensen, Danny C.
3 Toint, Philippe L.
3 Vlček, Jan
3 Wang, Yanfei
3 Yang, Weihong
3 Yang, Yufei
3 Ye, Yinyu
3 Zhang, Jianzhong
3 Zhou, Qinghua
3 Zhou, Shenglong
2 Adachi, Satoru
2 Ariyawansa, K. A.
2 Birgin, Ernesto G.
2 Brust, Johannes J.
2 Busygin, Stanislav
2 Conn, Andrew Roger
2 De Simone, Valentina
2 di Serafino, Daniela
2 Dussault, Jean-Pierre
2 El-Alem, Mahmoud M.
2 El-Sobky, Bothina
2 Fan, Jinyan
2 Fan, Shu-Kai S.
2 Ferris, Michael C.
2 Gao, Guohua
2 Gill, Philip E.
2 Griffin, Joshua D.
2 Hazan, Elad
2 Huo, Jiazhen
2 Ji, Ying
2 Karmarkar, Narendra K.
2 Koren, Tomer
2 Leyffer, Sven
2 Li, Donghui
2 Li, Junxiang
2 Lieder, Felix
2 Lin, Chih-Jen
2 Ling, Chen
2 Ma, Changfeng
2 Macconi, Maria
2 Matonoha, Ctirad
2 Menickelly, Matt
2 Mikhalevich, Vladimir Semenovich
2 Milz, Johannes
2 Monteiro, Renato D. C.
2 Moosaei, Hossein
2 Nakatsukasa, Yuji
2 Pardalos, Panos M.
2 Pasquali, Aldo
2 Pieraccini, Sandra
2 Pong, Ting Kei
2 Porcelli, Margherita
...and 377 more Authors
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Cited in 93 Serials

41 SIAM Journal on Optimization
33 Mathematical Programming. Series A. Series B
20 Computational Optimization and Applications
18 Journal of Global Optimization
15 Applied Mathematics and Computation
14 Journal of Computational and Applied Mathematics
12 Journal of Optimization Theory and Applications
7 SIAM Journal on Matrix Analysis and Applications
7 Linear Algebra and its Applications
7 SIAM Journal on Scientific Computing
7 Optimization Methods & Software
6 Optimization Letters
5 BIT
5 Applied Numerical Mathematics
4 Computers & Mathematics with Applications
4 SIAM Journal on Scientific and Statistical Computing
4 Journal of Computational Mathematics
4 Numerical Algorithms
4 European Journal of Operational Research
4 Computational Geosciences
4 Mathematical Programming Computation
3 Numerische Mathematik
3 Science in China. Series A
2 International Journal for Numerical Methods in Fluids
2 Inverse Problems
2 ACM Transactions on Mathematical Software
2 Computing
2 Journal of Econometrics
2 Kybernetika
2 Numerical Functional Analysis and Optimization
2 SIAM Journal on Numerical Analysis
2 Cybernetics
2 Operations Research Letters
2 RAIRO. Modélisation Mathématique et Analyse Numérique
2 Acta Mathematicae Applicatae Sinica. English Series
2 Journal of Scientific Computing
2 Annals of Operations Research
2 Journal of Statistical Computation and Simulation
2 Optimization and Engineering
2 Science China. Mathematics
1 Discrete Applied Mathematics
1 International Journal of Heat and Mass Transfer
1 International Journal of Mechanical Sciences
1 Journal of Mathematical Analysis and Applications
1 Mathematics of Computation
1 Applied Mathematics and Optimization
1 Automatica
1 International Journal of Mathematics and Mathematical Sciences
1 Mathematics of Operations Research
1 Operations Research
1 RAIRO. Recherche Opérationnelle
1 SIAM Journal on Control and Optimization
1 Optimization
1 Numerical Methods for Partial Differential Equations
1 Applied Mathematics Letters
1 Journal of Integral Equations and Applications
1 Machine Learning
1 Differential and Integral Equations
1 Applications of Mathematics
1 Computational Statistics
1 Applied Mathematical Modelling
1 International Journal of Computer Mathematics
1 Journal of Computer and Systems Sciences International
1 Applied Mathematics. Series B (English Edition)
1 Applied and Computational Harmonic Analysis
1 Computational and Applied Mathematics
1 Advances in Computational Mathematics
1 Abstract and Applied Analysis
1 Taiwanese Journal of Mathematics
1 Journal of Combinatorial Optimization
1 Journal of Applied Mathematics and Decision Sciences
1 PAA. Pattern Analysis and Applications
1 Acta Mathematica Sinica. English Series
1 CEJOR. Central European Journal of Operations Research
1 Far East Journal of Mathematical Sciences
1 RAIRO. Operations Research
1 CMES. Computer Modeling in Engineering & Sciences
1 Foundations of Computational Mathematics
1 Journal of Systems Science and Complexity
1 Journal of Machine Learning Research (JMLR)
1 Information
1 Journal of Applied Mathematics and Computing
1 REVSTAT
1 Acta Numerica
1 Journal of Industrial and Management Optimization
1 Frontiers of Mathematics in China
1 Applied Mathematical Sciences (Ruse)
1 Communications in Computational Physics
1 SIAM Journal on Imaging Sciences
1 GEM - International Journal on Geomathematics
1 Information and Inference
1 Bulletin of Computational Applied Mathematics
1 Springer Optimization and Its Applications

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