swMATH ID: 5141
Software Authors: Griewank, A.; Toint, Ph.L.
Description: On the unconstrained optimization of partially separable functions We consider the problem of minimizing a smooth objective function f of n real variables. For n>200 we can only hope to locate a local minimum of f within the usual limitations on storage and computing time by using a minimization algorithm that exploits some special structure of f. One such possibility is that the Hessian G(x) of f(x) has clustered eigenvalues at a minimizer x *, in which case conjugate gradient and limited memory variable metric methods were found to work quite well. However, in general, the performance of these methods is rather unpredictable since, except for certain test functions, the eigenvalue structure of G at or near x * is usually not known. Therefore we pursue the traditional approach of approximating f by local quadratic models, which is computationally feasible even for large n if f has a certain separability structure. This structure is always implied by sparsity of G, and depends only on the way in which the components of x enter into f, and not on the numerical values of f or its derivatives.
Homepage: http://www.netlib.org/opt/ve08
Keywords: partially separable functions; local approximation; smooth objective function
Related Software: LANCELOT; minpack; L-BFGS; CUTEr; CUTE; tn; AMPL; SifDec; ADIFOR; MINPACK-2; SNOPT; LIBSVM; Ipopt; ADOL-C; MINOS; SeDuMi; HSL; symrcm; CUTEst; CG_DESCENT
Cited in: 156 Documents
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Cited by 185 Authors

31 Toint, Philippe Louis
13 Yuan, Gonglin
10 Conn, Andrew Roger
9 Griewank, Andreas
9 Wei, Zengxin
8 Lukšan, Ladislav
6 Gould, Nick I. M.
5 Li, Donghui
5 Vlček, Jan
4 Fukushima, Masao
4 Kim, Sunyoung
4 Kojima, Masakazu
4 Matonoha, Ctirad
4 Nocedal, Jorge
4 Steihaug, Trond
3 Bischof, Christian H.
3 Goldfarb, Donald
3 Gould, Nicholas Ian Mark
3 Gundersen, Geir
3 Khademi, Peyvand M.
3 Li, Pengyuan
3 Martínez, José Mario
3 Nesterov, Yurii
3 Rodomanov, Anton
3 Stoer, Josef
2 Bidabadi, Narges
2 Bouaricha, Ali
2 Byrd, Richard H.
2 Cao, Huiping
2 Carle, Alan
2 Chen, Xiaojun
2 Dixon, Laurence C. W.
2 Fontecilla, Rodrigo
2 Gao, Wenbo
2 Gay, David M.
2 Gratton, Serge
2 Hossain, Shahadat
2 Kobayashi, Kazuhiro
2 Liu, Dongchang
2 Liu, Liying
2 Lu, Junyu
2 Lu, Xiwen
2 Ma, Xiaofang
2 Mahdavi-Amiri, Nezam
2 Martínez, Héctor Jairo
2 Moré, Jorge J.
2 Petra, Cosmin G.
2 Price, Christopher John
2 Qi, Liqun
2 Sartenaer, Annick
2 Sheng, Zhou
2 Tuyttens, Daniel
2 Xu, Chengxian
2 Yamashita, Nobuo
2 Yao, Shengwei
1 Absil, Pierre-Antoine
1 Aghezzaf, Brahim
1 Andrei, Neculai
1 Anitescu, Mihai
1 Ariyawansa, K. A.
1 Bagirov, Adil M.
1 Begashaw, Negash
1 Bongartz, Ingrid
1 Cartis, Coralia
1 Chen, Xiaoxuan
1 Chen, Zhong
1 Chiang, Naiyuan
1 Coleman, Thomas F.
1 Colson, Benoît
1 Dai, Yu-Hong
1 Daydé, Michel J.
1 De Baerdemaeker, Josse
1 Dennis, John E. jun.
1 Deussen, Jens
1 Dietze, Siegfried
1 Duintjer Tebbens, Jurjen
1 Dussault, Jean-Pierre
1 Engels, John R.
1 Eskow, Elizabeth
1 Fei, Pusheng
1 Feng, Haishan
1 Fletcher, Roger
1 Fung, Richard Ying Kit
1 Galli, Leonardo
1 Galligari, Alessandro
1 Gallivan, Kyle A.
1 Garbow, Burton S.
1 Gaur, Daya Ram
1 Gower, Robert Mansel
1 Haarala, M.
1 Han, Lixing
1 Hespanhol, Pedro
1 Hosseini Dehmiry, Alireza
1 Hu, Wujie
1 Huang, Wen
1 Hübner, Jens
1 Huchette, Joey
1 Huschens, J.
1 Janka, Dennis
1 Jin, Qiujiang
...and 85 more Authors
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Cited in 50 Serials

17 SIAM Journal on Optimization
13 Mathematical Programming. Series A. Series B
13 Optimization Methods & Software
7 Journal of Computational and Applied Mathematics
7 Computational Optimization and Applications
6 Numerical Algorithms
5 ACM Transactions on Mathematical Software
5 Journal of Optimization Theory and Applications
5 SIAM Journal on Numerical Analysis
4 Mathematics of Computation
4 Applied Mathematics and Computation
4 Kybernetika
3 Computing
3 Numerische Mathematik
3 Journal of Global Optimization
2 Mathematical Programming
2 Applied Numerical Mathematics
2 Computers & Operations Research
2 SIAM Journal on Scientific Computing
1 Computers & Mathematics with Applications
1 Discrete Applied Mathematics
1 Applied Mathematics and Optimization
1 Calcolo
1 Journal of the Korean Mathematical Society
1 Journal of the Operations Research Society of Japan
1 Numerical Functional Analysis and Optimization
1 SIAM Journal on Scientific and Statistical Computing
1 Journal of Computational Mathematics
1 Optimization
1 Constructive Approximation
1 Computational Statistics
1 Applied Mathematical Modelling
1 Numerical Linear Algebra with Applications
1 INFORMS Journal on Computing
1 Mathematical Problems in Engineering
1 Vychislitel’nye Tekhnologii
1 Acta Mathematica Sinica. English Series
1 Optimization and Engineering
1 Journal of Systems Science and Complexity
1 Acta Numerica
1 Computational Management Science
1 Journal of Industrial and Management Optimization
1 Journal of Applied Functional Analysis
1 Journal of the Korean Statistical Society
1 Springer Series in Computational Mathematics
1 Advanced Modeling and Optimization
1 Advances in Operations Research
1 Mathematical Programming Computation
1 Journal of the Operations Research Society of China

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