One way of solving these kinds of problems is the Raleigh-Ritz method.
Robert Dodier wrote:
>On 1/17/06, Daniel Lakeland <dlakelan at street-artists.org> wrote:
>
>
>
>>Is there a way to make the routines in the "optmiz" library find an
>>alternate point?
>>
>>
>
>not so far as i know.
>
>if i understand optmiz correctly, it formulates an augmented lagrangian
>(to reduce the problem to an unconstrained optimization) and then
>it calls the built-in solve function. so if solve returns multiple solutions,
>i guess optmiz has the opportunity to choose among them.
>maybe it wouldn't be too hard to modify optmiz to do that;
>maybe optmiz is already doing that.
>
>
>
>>Is there a canned numerical constrained optimizer routine?
>>
>>
>
>the only one that i know of is augmented_lagrangian.mac
>(which i wrote), which you can find here --
>http://cvs.sf.net/viewcvs.py/maxima/maxima/share/contrib/
>
>that script, like optmiz, forms an augmented lagrangian, but
>then it uses a numerical method to solve it.
>(the numerical method is to apply mnewton to grad L = 0;
>that is very weak. however, maxima doesn't have a numerical
>method for unconstrained optimization, which is a great lack.)
>
>(i started to port a quasi-newton minimizer from fortran to lisp,
>but i got sidetracked ... i should get back to that.)
>
>
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>>I recently used mnewton to do optimization with lagrange multipliers
>>so I know it can be done that way. but I don't want to reinvent the
>>wheel again if there's a better way.
>>
>>
>
>what did you do? it may well be an improvement over augmented_lagrangian.
>
>sorry i can't be more helpful. it is certainly possible i've
>overlooked something.
>
>robert dodier
>
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