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43.1 Definitions for augmented_lagrangian |
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Default value: 10
Number of iterations for augmented_lagrangian_method
.
Augmented Lagrangian method for constrained optimization. FOM is the figure of merit expression, xx is a list of variables over which to minimize, constraints is a list of expressions to be held equal to zero, and yy is a list of initial guesses for xx.
At present this code minimizes the augmented Lagrangian by solving for a stationary point of its gradient. That's pretty weak, and the code could be improved by plugging in a conjugate gradient or quasi-Newton minimization algorithm.
For references see
http://www-fp.mcs.anl.gov/otc/Guide/OptWeb/continuous/constrained/nonlinearcon/auglag.html |
and
http://www.cs.ubc.ca/spider/ascher/542/chap10.pdf |
Package mnewton
(to solve grad L = 0) has to be loaded before calling augmented_lagrangian_method
.
Example:
(%i1) load (mnewton)$ (%i2) load("augmented_lagrangian")$ (%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); (%o7) [0.6478349834, 0.3239174917] |
To use this function write first load("mnewton")
and load("augmented_lagrangian")
.
See also niter
.
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