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42.1 Functions and Variables for augmented_lagrangian |
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Returns an approximate minimum of the expression FOM with respect to the variables xx, holding the constraints C equal to zero. yy is a list of initial guesses for xx. The method employed is the augmented Lagrangian method (see Refs [1] and [2]).
optional_args
represents additional arguments,
specified as symbol = value
.
The optional arguments recognized are:
niter
Number of iterations of the augmented Lagrangian algorithm
lbfgs_tolerance
Tolerance supplied to LBFGS
iprint
IPRINT parameter (a list of two integers which controls verbosity) supplied to LBFGS
%lambda
Initial value of %lambda
to be used for calculating the augmented Lagrangian
This implementation minimizes the augmented Lagrangian by applying the limited-memory BFGS (LBFGS) algorithm, which is a quasi-Newton algorithm.
load(augmented_lagrangian)
loads this function.
See also lbfgs
.
References:
[1] http://www-fp.mcs.anl.gov/otc/Guide/OptWeb/continuous/constrained/nonlinearcon/auglag.html
[2] http://www.cs.ubc.ca/spider/ascher/542/chap10.pdf
Example:
(%i1) load (lbfgs); (%o1) /maxima/share/lbfgs/lbfgs.mac (%i2) load (augmented_lagrangian); (%o2) /maxima/share/contrib/augmented_lagrangian.mac (%i3) FOM: x^2 + 2*y^2; 2 2 (%o3) 2 y + x (%i4) xx: [x, y]; (%o4) [x, y] (%i5) C: [x + y - 1]; (%o5) [y + x - 1] (%i6) yy: [1, 1]; (%o6) [1, 1] (%i7) augmented_lagrangian_method(FOM, xx, C, yy, iprint=[-1,0]); (%o7) [[x = 0.66665984108002, y = 0.33334027245545], %lambda = [- 1.333337940892525]]
Categories: Numerical methods · Share packages · Package augmented_lagrangian
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