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New subspace minimization conjugate gradient methods based on regularization model for unconstrained optimization
- Source :
- Numerical Algorithms. 87:1501-1534
- Publication Year :
- 2020
- Publisher :
- Springer Science and Business Media LLC, 2020.
-
Abstract
- In this paper, two new subspace minimization conjugate gradient methods based on p-regularization models are proposed, where a special scaled norm in p-regularization model is analyzed. Different choices of special scaled norm lead to different solutions to the p-regularized subproblem. Based on the analyses of the solutions in a two-dimensional subspace, we derive new directions satisfying the sufficient descent condition. With a modified nonmonotone line search, we establish the global convergence of the proposed methods under mild assumptions. R-linear convergence of the proposed methods is also analyzed. Numerical results show that, for the CUTEr library, the proposed methods are superior to four conjugate gradient methods, which were proposed by Hager and Zhang (SIAM J. Optim. 16(1):170–192, 2005), Dai and Kou (SIAM J. Optim. 23(1):296–320, 2013), Liu and Liu (J. Optim. Theory. Appl. 180(3):879–906, 2019) and Li et al. (Comput. Appl. Math. 38(1):2019), respectively.
- Subjects :
- Line search
Applied Mathematics
Numerical analysis
010103 numerical & computational mathematics
01 natural sciences
Regularization (mathematics)
010101 applied mathematics
Conjugate gradient method
Norm (mathematics)
Theory of computation
Applied mathematics
Minification
0101 mathematics
Subspace topology
Mathematics
Subjects
Details
- ISSN :
- 15729265 and 10171398
- Volume :
- 87
- Database :
- OpenAIRE
- Journal :
- Numerical Algorithms
- Accession number :
- edsair.doi...........855c6889d265ebf9e513400e3b41ebe8