petsc-3.13.6 2020-09-29

SNESQN

Limited-Memory Quasi-Newton methods for the solution of nonlinear systems.

Options Database

	-snes_qn_m <m>	- Number of past states saved for the L-Broyden methods. + -snes_qn_restart_type <powell,periodic,none> - set the restart type
	-snes_qn_powell_gamma	- Angle condition for restart.
	-snes_qn_powell_descent	- Descent condition for restart.
	-snes_qn_type <lbfgs,broyden,badbroyden>	- QN type
	-snes_qn_scale_type <diagonal,none,scalar,jacobian>	- scaling performed on inner Jacobian
	-snes_linesearch_type <cp, l2, basic>	- Type of line search.
	-snes_qn_monitor	- Monitors the quasi-newton Jacobian.

Notes

This implements the L-BFGS, Broyden, and "Bad" Broyden algorithms for the solution of F(x) = b using previous change in F(x) and x to form the approximate inverse Jacobian using a series of multiplicative rank-one updates.

When using a nonlinear preconditioner, one has two options as to how the preconditioner is applied. The first of these options, sequential, uses the preconditioner to generate a new solution and function and uses those at this iteration as the current iteration's values when constructing the approximate Jacobian. The second, composed, perturbs the problem the Jacobian represents to be P(x, b) - x = 0, where P(x, b) is the preconditioner.

Uses left nonlinear preconditioning by default.

References

	1.	- Kelley, C.T., Iterative Methods for Linear and Nonlinear Equations, Chapter 8, SIAM, 1995.
	2.	- R. Byrd, J. Nocedal, R. Schnabel, Representations of Quasi Newton Matrices and their use in Limited Memory Methods, Technical Report, Northwestern University, June 1992.
	3.	- Peter N. Brown, Alan C. Hindmarsh, Homer F. Walker, Experiments with Quasi-Newton Methods in Solving Stiff ODE Systems, SIAM J. Sci. Stat. Comput. Vol 6(2), April 1985.
	4.	- Peter R. Brune, Matthew G. Knepley, Barry F. Smith, and Xuemin Tu, "Composing Scalable Nonlinear Algebraic Solvers", SIAM Review, 57(4), 2015
	5.	- Griewank, Andreas. "Broyden updating, the good and the bad!." Doc. Math (2012): 301-315.
	6.	- Gilbert, Jean Charles, and Claude Lemar{\'e}chal. "Some numerical experiments with variable-storage quasi-Newton algorithms." Mathematical programming 45.1-3 (1989): 407-435.
	7.	- Dener A., Munson T. "Accelerating Limited-Memory Quasi-Newton Convergence for Large-Scale Optimization" Computational Science - ICCS 2019. ICCS 2019. Lecture Notes in Computer Science, vol 11538. Springer, Cham

Level

beginner

Location