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HSL-VF05

swMATH ID: 36311
Software Authors: Gould, Nicholas I. M.; Lucidi, Stefano; Roma, Massimo; Toint, Philippe L.
Description: Solving the trust-region subproblem using the Lanczos method. The approximate minimization of a quadratic function within an ellipsoidal trust region is an important subproblem for many nonlinear programming methods. When the number of variables is large, the most widely used strategy is to trace the path of conjugate gradient iterates either to convergence or until it reaches the trust-region boundary. We investigate ways of continuing the process once the boundary has been encountered. The key is to observe that the trust-region problem within the currently generated Krylov subspace has a very special structure which enables it to be solved very efficiently. We compare the new strategy with existing methods. The resulting software package is available as HSL-VF05 within the Harwell Subroutine Library.
Homepage: https://www.researchgate.net/publication/2263739_Solving_the_Trust-Region_Subproblem_using_the_Lanczos_Method
Dependencies: HSL
Keywords: convergence acceleration; nonlinear systems; fixed point iteration; conjugate gradients; preconditioning
Related Software: GQTPAR; CUTEr; LSTRS; GALAHAD; SifDec; L-BFGS; CUTEst; tn; Ipopt; ARPACK; Regularization tools; LANCELOT; LBFGS-B; LAPACK; Mosek; SNOPT; SparseMatrix; MA57; LSQR; HSL
Cited in: 74 Publications
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Cited by 150 Authors

5 Gould, Nicholas Ian Mark
5 Shen, Chungen
5 Toint, Philippe L.
5 Zhang, Lei-Hong
4 Salahi, Maziar
4 Taati, Akram
3 Cartis, Coralia
3 Xia, Yong
3 Yang, Weihong
2 Burer, Samuel
2 Carmon, Yair
2 Duchi, John C.
2 Erway, Jennifer B.
2 Griffin, Joshua D.
2 Kılınç Karzan, Fatma
2 Marcia, Roummel F.
2 Nakatsukasa, Yuji
2 Pong, Ting Kei
2 Robinson, Daniel P.
2 Roma, Massimo
2 Wang, Jiulin
2 Yang, Boshi
2 Zhu, Detong
1 Adachi, Satoru
1 Agarwal, Naman
1 Ahookhosh, Masoud
1 Akrotirianakis, Ioannis G.
1 Apostolopoulou, M. S.
1 Beck, Amir
1 Bellis, Cédric
1 Belotti, Pietro
1 Bergou, El Houcine
1 Bianconcini, Tommaso
1 Botsaris, C.-A. E.
1 Boumal, Nicolas
1 Brás, Carmo P.
1 Brossier, Romain
1 Bullins, Brian
1 Burdakov, Oleg P.
1 Chiang, Naiyuan
1 Chieu, Nguyen Huy
1 Curtis, Frank E.
1 Dang, Chuangying
1 D’Apuzzo, Marco
1 De Simone, Valentina
1 di Serafino, Daniela
1 Diouane, Youssef
1 Eldén, Lars
1 Fasano, Giovanni
1 Fatemi, Masoud
1 Feng, Jiang
1 Fourer, Robert
1 Frangioni, Antonio
1 Furini, Fabio
1 Ghaderi, Susan
1 Gleixner, Ambros M.
1 Gong, Lujin
1 Goulart, Paul J.
1 Gould, Nick I. M.
1 Gratton, Serge
1 Hager, William W.
1 Hansen, Per Christian
1 Hazan, Elad
1 Higham, Nicholas J.
1 Ho-Nguyen, Nam
1 Hoffmann, Alexandre
1 Hou, Liusheng
1 Huang, Baohua
1 Jia, Chunxia
1 Jia, Xiaojing
1 Jia, Zhongxiao
1 Júdice, Joaquim João
1 Kirches, Christian
1 Kolvenbach, Philip
1 Koren, Tomer
1 Lass, Oliver
1 Le Van Hien
1 Lenders, Felix
1 Li, Rencang
1 Liang, Xin
1 Liberti, Leo
1 Liuzzi, Giampaolo
1 Lodi, Andrea
1 Lu, Zhaosong
1 Lucidi, Stefano
1 Lukšan, Ladislav
1 Ma, Changfeng
1 Mahdavi-Amiri, Nezam
1 Mahoney, Michael W.
1 Martínez, José Mario
1 Matonoha, Ctirad
1 Métivier, Ludovic
1 Misener, Ruth
1 Mittelmann, Hans Detlef
1 Monteiller, Vadim
1 Monteiro, Renato D. C.
1 Morigi, Serena
1 Morini, Benedetta
1 Nash, Stephen G.
1 Nguyen, Thi Ngan
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