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 1014.65050Powell, M. J. D. 2002 all top 5 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 all top 5 Cited in 32 Serials 8 Journal of Global Optimization 5 Journal of Computational and Applied Mathematics 5 Mathematical Programming. Series A. Series B 5 Optimization Methods & Software 4 SIAM Journal on Optimization 3 European Journal of Operational Research 3 Computational Optimization and Applications 3 Computational and Applied Mathematics 3 Optimization and Engineering 2 Optimization Letters 2 Mathematical Programming Computation 1 IMA Journal of Numerical Analysis 1 Journal of Computational Physics 1 ACM Transactions on Mathematical Software 1 Automatica 1 Journal of Economic Theory 1 Acta Mathematicae Applicatae Sinica. English Series 1 Computers & Operations Research 1 Science in China. Series A 1 Numerical Algorithms 1 Turkish Journal of Mathematics 1 Far East Journal of Applied Mathematics 1 Computational Geosciences 1 Journal of Applied Mathematics and Computing 1 Structural and Multidisciplinary Optimization 1 Acta Numerica 1 CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC 1 Advances in Applied Mathematics and Mechanics 1 Set-Valued and Variational Analysis 1 Numerical Algebra, Control and Optimization 1 Stochastic Systems 1 EURO Journal on Computational Optimization all top 5 Cited in 11 Fields 63 Operations research, mathematical programming (90-XX) 28 Numerical analysis (65-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 3 Statistics (62-XX) 2 Ordinary differential equations (34-XX) 1 Partial differential equations (35-XX) 1 Probability theory and stochastic processes (60-XX) 1 Fluid mechanics (76-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Geophysics (86-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year