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Howtonotwin (talk | contribs) m →Potential-reduction methods: replace norse rune(!!) with the intersection symbol |
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=== Practical considerations ===
The theoretic guarantees assume that the penalty parameter is increased at the rate <math>\mu = \left(1+r/\sqrt{M}\right)</math>, so the worst-case number of required Newton steps is <math>O(\sqrt{M})</math>. In theory, if ''μ'' is larger (e.g. 2 or more), then the worst-case number of required Newton steps is in <math>O(M)</math>. However, in practice, larger ''μ'' leads to a much faster convergence. These methods are called ''long-step methods''.<ref name=":0" />{{Rp|___location=Sec.4.6}} In practice, if ''μ'' is between 3 and 100, then the program converges within 20-40 Newton steps, regardless of the number of constraints (though the runtime of each Newton step of course grows with the number of constraints). The exact value of ''μ'' within this range has little effect on the
== Potential-reduction methods ==
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