References
- Wei Z, Li G, Qi L. New quasi-Newton methods for unconstrained optimization problems. Appl Math Comput. 2006;175(2):1156–1188.
- Zhang JZ, Deng NY, Chen LH. New Quasi-Newton equation and related methods for unconstrained optimization. J Optim Theory Appl. 1999;102(1):147–167. doi: 10.1023/A:1021898630001
- Schnabel RB, Chow TT. Tensor methods for unconstrained optimization using second derivatives. SIAM J Optim. 1991;1(3):293–315. doi: 10.1137/0801020
- Ford JA, Moghrabi IA. Multi-step quasi-Newton methods for optimization. J Comput Appl Math. 1994;50(1):305–323. doi: 10.1016/0377-0427(94)90309-3
- Spedicato E. A class of rank-one positive definite quasi-Newton updates for unconstrained minimization 2. Optimization. 1983;14(1):61–70.
- Yuan Y. A modified BFGS algorithm for unconstrained optimization. IMA J Numer Anal. 1991;11(3):325–332. doi: 10.1093/imanum/11.3.325
- Davidon WC. Conic approximations and collinear scalings for optimizers. SIAM J Numer Anal. 1980;17(2):268–281. doi: 10.1137/0717023
- Dennis Jr JE, Gay DM, Welsch RE. Algorithm 573: NL2SOLan adaptive nonlinear least-squares algorithm [E4]. ACM Trans Math Software (TOMS). 1981;7(3):369–383. doi: 10.1145/355958.355966
- Enshaei S, June Leong W, Farid M. Diagonal quasi-Newton method via variational principle under generalized Frobenius norm. Optim Methods Softw. 2016;31(6):1258–1271. doi: 10.1080/10556788.2016.1196205
- Wei Z, Qi L, Jiang H. Some convergence properties of descent methods. J Optim Theory Appl. 1997;95(1):177–188. doi: 10.1023/A:1022691513687
- Wei Z, Qi L, Ito S. New step-size rules for optimization problems. Nanning: Department of Mathematics and Information Science, Guangxi University; 2000.
- Leong WJ, Farid M, Hassan MA. Scaling on diagonal Quasi-Newton update for large-scale unconstrained optimization. Bull Malays Math Sci Soc. 2012;35(2):247–256.
- Khalfan HF, Byrd RH, Schnabel RB. A theoretical and experimental study of the symmetric rank-one update. SIAM J Optim. 1993;3(1):1–24. doi: 10.1137/0803001
- Byrd RH, Schnabel RB, Shultz GA. A trust region algorithm for nonlinearly constrained optimization. SIAM J Numer Anal. 1987;24(5):1152–1170. doi: 10.1137/0724076
- Hardy GH, Littlewood JE, Pólya G. Inequalities. Cambridge (UK): Cambridge University Press; 1952.
- Dolan ED, Moré JJ. Benchmarking optimization software with performance profiles. Math Program. 2002;91(2):201–213. doi: 10.1007/s101070100263
- Hager WW, Zhang H. The limited memory conjugate gradient method. SIAM J Optim. 2013;23(4):2150–2168. doi: 10.1137/120898097
- Gilbert JC, Nocedal J. Global convergence properties of conjugate gradient methods for optimization. SIAM J Optim. 1992;2(1):21–42. doi: 10.1137/0802003