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hart@de01.denver.waii.com said:
>
>Multiplier methods, for constrained optimization problems, generally
>exceed the performance of penalty function methods.  The reference:
>R.A. Tapia, "Diagonalized Multiplier Methods and Quasi-Newton Methods for
>Constrainded Optimization", Journal of Optimization Theory and Applications,
>Vol. 22., No.2, June 1977, p. 135-194., is where I got started with these
>methods.  Two papers on Penalty Function methods are in the reference section
>of this paper.  They should point you to some examples of penalty functions.


Multiplier methods are fine for *continuous* optimization, but not readily
applicable for many combinatorial problems, unless a convenient continuous
relaxation exists.  Multiplier methods also require that you have an explicit
representation of the constraint set in a particular form.  For example, in
a Travelling Salesman problem the logically simply constraint "Each tour must
pass through each city exactly once" translates into an exponential number of
linear inequalities in the linear/integer programming formulation.

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