`a`
Journal of Industrial and Management Optimization (JIMO)
 

A modified scaled memoryless BFGS preconditioned conjugate gradient algorithm for nonsmooth convex optimization
Page number are going to be assigned later 2017

doi:10.3934/jimo.2017075      Abstract        References        Full text (405.7K)      

Yigui Ou - Department of Applied Mathematics, Hainan University, Haikou 570228, China (email)
Xin Zhou - Department of Applied Mathematics, Hainan University, Haikou 570228, China (email)

1 N. Andrei, Scaled conjugate gradient algorithms for unconstrained optimization, Computational Optimization and Applications, 38 (2007), 401-416.       
2 A. Auslender, Numerical methods for nondifferentiable convex optimization, Mathematical Programming Study, 30 (1987), 102-126.       
3 S. Babaie-Kafaki, A modified scaled memoryless BFGS preconditioned conjugate gradient method for unconstrained optimization, 4OR, A Quarterly Journal of Operations Research, 11 (2013), 361-374.       
4 S. Babaie-Kafaki and R. Chanbari, A class of descent four-term extension of the Dai-Liao conjugate gradient method based on the scaled memoryless BFGS update, Journal of Industrial and Management Optimization, 13 (2017), 649-658.       
5 J. Barzilai and J. M. Borwein, Two-point stepsize gradient methods, IMA Journal of Numerical Analysis, 8 (1988), 141-148.
6 E. Birgin and J. M. Martínez, A spectral conjugate gradient method for unconstrained optimization, Applied Mathematics and Optimization, 43 (2001), 117-128.       
7 J. F. Bonnans, J. C. Gilbert, C. Lemarechal and C. Sagastizabal, A family of variable-metric proximal methods, Mathematical Programming, 68 (1995), 15-47.       
8 J. V. Burke and M. Qian, On the superlinear convergence of the variable metric proximal point algorithm using Broyden and BFGS matrix secant updating, Mathematical Programming, 88 (2000), 157-181.       
9 X. Chen and M. Fukushima, Proximal quasi-Newton methods for nondifferentiable convex optimization, Mathematical Programming, 85 (1999), 313-334.       
10 E. D. Dolan and J. J. Moré, Benchmarking optimization software with performance profiles, Mathematical Programming, Serial A, 91 (2002), 201-213.       
11 M. Fukushima, A descent algorithm for nonsmooth convex optimization, Mathematical Programming, 30 (1984), 163-175.       
12 M. Fukushima and L. Q. Qi, A globally and superlinearly convergent algorithm for nonsmooth convex minimization, SIAM Journal on Optimization, 6 (1996), 1106-1120.       
13 M. Haarala, K. Miettinen and M. M. Mäkelä, New limited memory bundle method for large-scale nonsmooth optimization, Optimization Methods and Software, 19 (2004), 673-692.       
14 M. Haarala, K. Miettinen and M. M. Mäkelä, Globally convergent limited memory bundle method for large-scale nonsmooth optimization, Mathematical Programming, 109 (2007), 181-205.       
15 W. W. Hager and H. C. Zhang, A survey of nonlinear conjugate gradient methods, Pacific Journal of Optimization, 2 (2006), 35-58.       
16 J. B. Hiriart-Urruty and C. Lemaréchal, Convex Analysis and Minimization Algorithms, Springer, Berlin, 1993.
17 C. Lemarechal and C. Sagastizabal, Practical aspects of the Moreau-Yosida regularization, I: Theoretical preliminaries, SIAM Journal on Optimization, 7 (1997), 367-385.       
18 Q. Li, Conjugate gradient type methods for the nondifferentiable convex minimization, Optimization Letters, 7 (2013), 533-545.       
19 D. H. Li and M. Fukushima, A derivative-free line search and global convergence of Broyden-like method for nonlinear equations, Optimization Methods and Software, 13 (2000), 181-201.       
20 S. Lu, Z. X. Wei and L. Li, A trust region algorithm with adaptive cubic regularization methods for nonsmooth convex minimization, Computational Optimization and Applications, 51 (2012), 551-573.       
21 L. Lukšan and J. Vlček, Test Problems for Nonsmooth Unconstrained and Linearly Constrained Optimization, Technical Report No. 798, Institute of Computer Science, Academy of Sciences of the Czech Republic, 2000.
22 R. Mifflin, A quasi-second-order proximal bundle algorithm, Mathematical Programming, 73 (1996), 51-72.
23 Y. G. Ou and H. C. Lin, An ODE-like nonmonotone method for nonsmooth convex optimization, Journal of Applied Mathematics and Computing, 52 (2016), 265-285.       
24 L. Q. Qi, Convergence analysis of some algorithms for solving nonsmooth equations, Mathematics of Operations Research, 18 (1993), 227-244.       
25 A. I. Rauf and M. Fukushima, A globally convergent BFGS method for nonsmooth convex optimization, Journal of Optimization Theory and Applications, 104 (2000), 539-558.       
26 N. Sagara and M. Fukushima, A trust region method for nonsmooth convex optimization, Journal of Industrial and Management Optimization, 1 (2005), 171-180.       
27 D. F. Shanno, On the convergence of a new conjugate gradient algorithm, SIAM Journal on Numerical Analysis, 15 (1978), 1247-1257.       
28 J. Shen, L. P. Pang and D. Li, An approximate quasi-Newton bundle-type method for nonsmooth optimization, Abstract and Applied Analysis, 2013, Art. ID 697474, 7 pp.       
29 W. Y. Sun and Y. X. Yuan, Optimization Theory and Methods: Nonlinear Programming, Springer, New York, 2006.       
30 G. L. Yuan, Z. H. Meng and Y. Li, A modified Hestenes and Stiefel conjugate gradient algorithm for large scale nonsmooth minimizations and nonlinear equations, Journal of Optimization Theory and Applications, 168 (2016), 129-152.       
31 G. L. Yuan, Z. Sheng and W. J. Liu, The modified HZ conjugate gradient algorithm for large scale nonsmooth optimization, Plos One, 11 (2016), e0164289, 15pp.
32 G. L. Yuan and Z. X. Wei, The Barzilai and Borwein gradient method with nonmonotone line search for nonsmooth convex optimization problems, Mathematical Modelling and Analysis, 17 (2012), 203-216.       
33 G. L. Yuan, Z. X. Wei and G. Y. Li, A modified Polak-Ribière-Polyak conjugate gradient algorithm for nonsmooth convex programs, Journal of Computational and Applied mathematics, 255 (2014), 86-96.       
34 G. L. Yuan, Z. X. Wei and Z. X. Wang, Gradient trust region algorithm with limited memory BFGS update for nonsmooth convex minization, Computational Optimization and Applications, 54 (2013), 45-64.       
35 H. C. Zhang and W. W. Hager, A nonmonotone line search technique and its application to unconstrained optimization, SIAM Jpournal on Optimization, 14 (2004), 1043-1056.       
36 L. Zhang, W. J. Zhou and D. H. Li, A descent modified Polak-Ribière-Polyak conjugate gradient method and its global convergence, IMA Journal of Numerical Analysis, 26 (2006), 629-640.       

Go to top