The semi-smooth Newton method for solving problems of the following
structure:
System Message: WARNING/2 (\begin{split}
& F(y) = 0 \\
& A(y) \ge 0 \;,\ B(y) \ge 0 \;,\ \langle A(y), B(y) \rangle = 0
\end{split}
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The function
System Message: WARNING/2 (F(y))
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represents the smooth part of the problem.
Regular step:
System Message: WARNING/2 (y \leftarrow y - J(y)^{-1} \Phi(y))
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LaTeX2e <2011/06/27>
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Document Class: article 2007/10/19 v1.4h Standard LaTeX document class
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Steepest descent step:
System Message: WARNING/2 (y \leftarrow y - \beta J(y) \Phi(y))
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This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/TeX Live for SUSE Linux)
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(./math.tex
LaTeX2e <2011/06/27>
Babel <3.9f> and hyphenation patterns for 78 languages loaded.
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Document Class: article 2007/10/19 v1.4h Standard LaTeX document class
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Notes
Although fun_smooth_grad() computes the gradient of the smooth part only,
it should return the global matrix, where the non-smooth part is
uninitialized, but pre-allocated.
-
compute_jacobian(vec_x, fun_smooth_grad, fun_a_grad, fun_b_grad, vec_smooth_r, vec_a_r, vec_b_r)[source]
-
name = 'nls.semismooth_newton'
-
static
process_conf(conf, kwargs)[source]
Missing items are set to default values.
Example configuration, all items:
solver_1 = {
'name' : 'semismooth_newton',
'kind' : 'nls.semismooth_newton',
'semismooth' : True,
'i_max' : 10,
'eps_a' : 1e-8,
'eps_r' : 1e-2,
'macheps' : 1e-16,
'lin_red' : 1e-2, # Linear system error < (eps_a * lin_red).
'ls_red_reg' : 0.1,
'ls_red_alt' : 0.01,
'ls_red_warp' : 0.001,
'ls_on' : 0.9,
'ls_min' : 1e-10,
'log' : {'plot' : 'convergence.png'},
}
