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UOBYQA

swMATH ID: 7576
Software Authors: Powell, M.J.D.
Description: UOBYQA: unconstrained optimization by quadratic approximation. A new algorithm for general unconstrained optimization calculations is described. It takes account of the curvature of the objective function by forming quadratic models by interpolation. Obviously, no first derivatives are required. A typical iteration of the algorithm generates a new vector of variables either by minimizing the quadratic model subject to a trust region bound, or by a procedure that should improve the accuracy of the model. The paper addresses the initial positions of the interpolation points and the adjustment of trust region radii. par The algorithm works with the Lagrange functions of the interpolation equations explicitly; therefore their coefficients are updated when an interpolation point is moved. The Lagrange functions assist the procedure that improves the model and also they provide an estimate of the error of the quadratic approximation of the function being minimized. It is pointed out that results are very promising for functions with less than twenty variables.
Homepage: http://rd.springer.com/article/10.1007%2Fs101070100290
Keywords: unconstrained optimization; quadratic approximation; trust region method; error bounds; algorithm
Related Software: DFO; NEWUOA; BOBYQA; COBYLA2; WEDGE; KELLEY; ORBIT; EGO; CONDOR; Matlab; GQTPAR; Boosters; MultiMin; NOMAD; minpack; IMFIL; SifDec; CUTEr; TOMLAB; MLMSRBF
Cited in: 67 Publications

Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
UOBYQA: unconstrained optimization by quadratic approximation. Zbl 1014.65050
Powell, M. J. D.
2002
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Cited by 133 Authors

6 Regis, Rommel G.
5 Gao, David Yang
4 Shoemaker, Christine A.
3 Scheinberg, Katya
3 Zhou, Qinghua
2 Brekelmans, Ruud C. M.
2 den Hertog, Dick
2 Driessen, Lonneke
2 Hamers, Herbert
2 Hare, Warren L.
2 Karas, Elizabeth W.
2 Larson, Jeffrey
2 Menickelly, Matt
2 Nocedal, Jorge
2 Powell, Michael James David
2 Sahinidis, Nikolaos V.
2 Wild, Stefan M.
2 Zhu, Jinghao
1 Ahmadvand, Mohammad
1 Ali, Montaz M.
1 Amos, Brandon D.
1 Arouxét, Ma. Belén
1 Audet, Charles
1 Bagirov, Adil M.
1 Bai, Fusheng
1 Berahas, Albert S.
1 Bersini, Hugues
1 Billups, Stephen C.
1 Birgin, Ernesto G.
1 Braun, Phillip A.
1 Byrd, Richard H.
1 Cartis, Coralia
1 Casella, Francesco
1 Castle, Brent S.
1 Chen, Xiaojun
1 Colson, Benoît
1 Conn, Andrew Roger
1 Dai, Yu-Hong
1 de Sampaio, Raimundo J. B.
1 Deng, Geng
1 Dolinskaya, Irina S.
1 Easterling, David R.
1 Echebest, Nélida E.
1 Esmaeilbeigi, Mohsen
1 Fagiano, Lorenzo Mario
1 Fasano, Giovanni
1 Ferreira, Priscila S.
1 Ferris, Michael C.
1 Geng, Yan
1 Gobbi, Paula E.
1 Gumma, E. A. E.
1 Ha, Minghu
1 Han, Lixing
1 Hare, W.
1 Hashemi, Fatemeh S.
1 Hashim, Mohsin Hassan Abdallah
1 He, Xinyu
1 Henderson, Shane G.
1 Hosseini, Mohammad-Mehdi
1 Hu, Yangzhou
1 Huang, Yunqing
1 Ihaddadene, Amina
1 Jarre, Florian
1 Jarry-Bolduc, Gabriel
1 Jiang, Cui
1 Jiang, Kai
1 Jiang, Zonglin
1 Kamandi, Ahmad
1 Kelley, Carl T.
1 Kimiaei, Morteza
1 Kolvenbach, Philip
1 Lass, Oliver
1 Le Digabel, Sébastien
1 Li, Gaoming
1 Li, Yan
1 Lieder, Felix
1 Liu, Guanghui
1 Liu, Hao
1 Luo, Changtong
1 Maalek Ghaini, Farid Mohammad
1 Maggiar, Alvaro
1 Manno, Andrea
1 Martelli, Emanuele
1 Martínez, José Mario
1 Maxwell, Matthew S.
1 Morales, José Luis
1 Nazareth, John Lawrence
1 Neumaier, Arnold
1 Ni, Qin
1 Pasupathy, Raghu
1 Pedroso, Lucas Garcia
1 Pilotta, Elvio A.
1 Pintér, János D.
1 Ploskas, Nikolaos
1 Powell, Warren Buckler
1 Rahmanpour, Fardin
1 Reynolds, Albert C. jun.
1 Rios, Luis Miguel
1 Roberts, Lindon
1 Ruiz, Fredy
...and 33 more Authors

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