TRON swMATH ID: 4714 Software Authors: Chih-Jen Lin; Jorge Moré Description: TRON is a trust region Newton method for the solution of large bound-constrained optimization problems. TRON uses a gradient projection method to generate a Cauchy step, a preconditioned conjugate gradient method with an incomplete Cholesky factorization to generate a direction, and a projected search to compute the step. The use of projected searches, in particular, allows TRON to examine faces of the feasible set by generating a small number of minor iterates, even for problems with a large number of variables. As a result TRON is remarkably efficient at solving large bound-constrained optimization problems. Homepage: http://www.mcs.anl.gov/~more/tron/ Related Software: L-BFGS; LBFGS-B; CUTEr; LANCELOT; L-BFGS-B; KELLEY; SNOPT; KNITRO; tn; Ipopt; LOQO; CUTE; CUTEst; SifDec; GQTPAR; SPG; GALAHAD; LIBSVM; MINPACK-2; NNLS Referenced in: 116 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Newton’s method for large bound-constrained optimization problems. Zbl 0957.65064Lin, Chih-Jen; Moré, Jorge J. 1999 all top 5 Referenced by 204 Authors 6 Lin, Chih-Jen 6 Nocedal, Jorge 6 Orban, Dominique 5 Haber, Eldad 4 Li, Donghui 4 Martínez, José Mario 4 Toint, Philippe L. 4 Xiao, Yunhai 3 Byrd, Richard H. 3 Cheng, Wanyou 3 Hager, William W. 3 Kanzow, Christian 3 Tenorio, Luis 3 Wei, Zengxin 3 Xiu, Naihua 3 Zhang, Jianzhong 2 Bellavia, Stefania 2 Birgin, Ernesto G. 2 Curtis, Frank E. 2 Friedlander, Michael P. 2 Gill, Philip E. 2 Gould, Nicholas Ian Mark 2 He, Guoping 2 Horesh, Lior 2 Klug, Andreas 2 Kouri, Drew P. 2 Kunisch, Karl 2 Leyffer, Sven 2 Lin, Lu 2 Lucidi, Stefano 2 Macconi, Maria 2 Morales, José Luis 2 Morini, Benedetta 2 Nash, Stephen G. 2 Peyghami, Mohammad Reza 2 Pytlak, Radosław 2 Sciandrone, Marco 2 Sra, Suvrit 2 Sun, Li 2 Ulbrich, Michael 2 Waltz, Richard A. 2 Wang, Yongli 2 Weng, Ruby Chiu-Hsing 2 Yuan, Gonglin 2 Zhang, Hongchao 1 Ahookhosh, Masoud 1 Andreani, Roberto 1 Anitescu, Mihai 1 Ariyawansa, K. A. 1 Arora, Nikhil 1 Arreckx, Sylvain 1 Austin, Anthony P. 1 Bagheri, Alireza 1 Bank, Randolph E. 1 Barbero, Álvaro 1 Bardsley, Johnathan M. 1 Belachew, Melisew Tefera 1 Biegler, Lorenz T. 1 Bonettini, Silvia 1 Bottou, Léon 1 Bui-Thanh, Tan 1 Burdakov, Oleg P. 1 Cafieri, Sonia 1 Caliciotti, Andrea 1 Cassioli, Andrea 1 Caudillo-Mata, Luz Angélica 1 Chang, Ming-Wei 1 Chen, Huajie 1 Chen, Jun 1 Chen, Tianyi 1 Chen, Zixin 1 Chin, Gillian M. 1 Chu, Yingyi 1 Chung, Kai-Min 1 Cortés, J. J. 1 Cristofari, Andrea 1 Dahito, Marie-Ange 1 D’Apuzzo, Marco 1 De Baets, Bernard 1 de Sampaio, Raimundo J. B. 1 De Santis, Marianna 1 De Simone, Valentina 1 Dhillon, Inderjit S. 1 di Serafino, Daniela 1 Di, Zichao 1 Dong, Junliang 1 Ek, David 1 Erway, Jennifer B. 1 Estrin, Ron 1 Facchinei, Francisco 1 Fan, Changxing 1 Fang, Liang 1 Fasano, Giovanni 1 Felt, Andrew J. 1 Forsgren, Anders 1 Gao, Junbin 1 Gavrea, Bogdan I. 1 Ghattas, Omar N. 1 Gillis, Nicolas 1 Good, Marcel ...and 104 more Authors all top 5 Referenced in 46 Serials 10 SIAM Journal on Optimization 10 Computational Optimization and Applications 8 Journal of Optimization Theory and Applications 7 Journal of Computational and Applied Mathematics 6 Optimization Methods & Software 5 Computers & Mathematics with Applications 5 Mathematical Programming. Series A. Series B 5 SIAM Journal on Scientific Computing 4 Applied Mathematics and Computation 3 Inverse Problems 3 Numerische Mathematik 3 Optimization Letters 2 IMA Journal of Numerical Analysis 2 Applied Numerical Mathematics 2 Neural Computation 2 Applied Mathematical Modelling 2 Numerical Linear Algebra with Applications 2 Computational and Applied Mathematics 2 Mathematical Methods of Operations Research 2 Optimization and Engineering 2 Journal of Machine Learning Research (JMLR) 1 Computer Methods in Applied Mechanics and Engineering 1 ACM Transactions on Mathematical Software 1 Operations Research Letters 1 Optimization 1 Mathematical and Computer Modelling 1 Annals of Operations Research 1 Machine Learning 1 Applications of Mathematics 1 Journal of Global Optimization 1 Linear Algebra and its Applications 1 SIAM Review 1 Computational Statistics and Data Analysis 1 Advances in Mathematical Sciences and Applications 1 Revista Investigación Operacional 1 INFORMS Journal on Computing 1 Journal of Applied Mathematics and Decision Sciences 1 Far East Journal of Applied Mathematics 1 Journal of Systems Science and Complexity 1 4OR 1 Acta Numerica 1 Nonconvex Optimization and Its Applications 1 Inverse Problems and Imaging 1 SIAM Journal on Imaging Sciences 1 Numerical Mathematics: Theory, Methods and Applications 1 Science China. Mathematics all top 5 Referenced in 21 Fields 90 Operations research, mathematical programming (90-XX) 67 Numerical analysis (65-XX) 19 Calculus of variations and optimal control; optimization (49-XX) 8 Computer science (68-XX) 7 Statistics (62-XX) 6 Information and communication theory, circuits (94-XX) 5 Partial differential equations (35-XX) 4 Mechanics of deformable solids (74-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Geophysics (86-XX) 2 Systems theory; control (93-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of particles and systems (70-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) 1 Quantum theory (81-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Astronomy and astrophysics (85-XX) 1 Biology and other natural sciences (92-XX) 1 Mathematics education (97-XX) Referencing Publications by Year