GQTPAR swMATH ID: 7451 Software Authors: Moré, Jorge J.; Sorensen, D.C. Description: Computing a trust region step We propose an algorithm for the problem of minimizing a quadratic function subject to an ellipsoidal constraint and show that this algorithm is guaranteed to produce a nearly optimal solution in a finite number of iterations. We also consider the use of this algorithm in a trust region Newton’s method. In particular, we prove that under reasonable assumptions the sequence generated by Newton’s method has a limit point which satisfies the first and second order necessary conditions for a minimizer of the objective function. Numerical results for GQTPAR, which is a Fortran implementation of our algorithm, show that GQTPAR is quite successful in a trust region method. In our tests a call to GQTPAR only required 1.6 iterations on the average. Homepage: http://epubs.siam.org/doi/abs/10.1137/0904038 Keywords: Newton’s method; trust region; ellipsoidal constraint; global convergence Related Software: HSL-VF05; CUTEr; minpack; LSTRS; LANCELOT; Matlab; L-BFGS; SifDec; GALAHAD; Regularization tools; CUTEst; ARPACK; UOBYQA; DFO; tn; NEWUOA; LAPACK; KELLEY; CUTE; MSS Cited in: 333 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Computing a trust region step. Zbl 0551.65042Moré, Jorge J.; Sorensen, D. C. 1983 all top 5 Cited by 477 Authors 14 Yuan, Ya-xiang 11 Zhu, Detong 8 Kanzow, Christian 8 Shen, Chungen 8 Zhang, Lei-Hong 7 Beck, Amir 7 Erway, Jennifer B. 7 Lukšan, Ladislav 7 Moré, Jorge J. 7 Schnabel, Robert B. 7 Wolkowicz, Henry 7 Xia, Yong 6 Coleman, Thomas F. 6 Gould, Nicholas Ian Mark 6 Li, Duan 6 Marcia, Roummel F. 6 Qi, Liqun 6 Salahi, Maziar 5 Bellavia, Stefania 5 Jiang, Rujun 5 Martínez, José Mario 5 Morini, Benedetta 5 Pham Dinh Tao 5 Xiu, Naihua 4 Abdel-Aziz, Mohammedi R. 4 Byrd, Richard H. 4 Qi, Houduo 4 Robinson, Daniel P. 4 Sun, Wenyu 4 Taati, Akram 4 Vicente, Luis Nunes 3 Ben-Tal, Aharon 3 Burer, Samuel 3 Chu, Delin 3 Chu, Moody T. 3 Curtis, Frank E. 3 Fukushima, Masao 3 Guan, Yu 3 Jian, Jinbao 3 Kılınç Karzan, Fatma 3 Larson, Jeffrey 3 Le Thi, Hoai An 3 Li, Rencang 3 Li, Yuying 3 Mai-Duy, Nam 3 Ni, Qin 3 Reichel, Lothar 3 Santos, Sandra Augusta 3 Sorensen, Danny C. 3 Toint, Philippe L. 3 Vlček, Jan 3 Wang, Yanfei 3 Yang, Weihong 3 Yang, Yufei 3 Ye, Yinyu 3 Zhang, Jianzhong 3 Zhou, Qinghua 3 Zhou, Shenglong 2 Adachi, Satoru 2 Ariyawansa, K. 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