
Re: Problem with NMaximize
Posted:
Jun 28, 2008 5:58 AM


ramiro wrote: > Thank you very much for your responses, Bobby and JeanMarc. I did try > changing the parametrization (thanks Bobby!) and I got an answer. > > However, let me try again with a hopefully more clear example, as I > don't understand why this doesn't work, in particular, I don't > understand why is it evaluating negative numbers if I am putting as a > constraint that it shouldn't? > > > Sample likelihood, > > In[196]:= > logLikelihood1[t1_?NumberQ, t2_?NumberQ, t3_?NumberQ, t4_?NumberQ, > t5_?NumberQ, t6_?NumberQ, t7_?NumberQ, t8_?NumberQ, t9_?NumberQ, > t10_?NumberQ, t11_?NumberQ, t12_?NumberQ] := > Log[0.00001712341312000713` t1 + 5.648647024829866`*^6 t10 + > 8.90597537441381`*^6 t11 + 1.9727284288726167`*^6 t12 + > 4.102725237468317`*^6 t2 + 3.7864902508468615`*^6 t3 + > 9.215772325326653`*^7 t4 + 0.000057161484895917856` t5 + > 0.000012892953334779516` t6 + 8.646320198720343`*^6 t7 + > 5.877910295858781`*^6 t8 + 1.6837835562631724`*^6 t9]; > [...] > In[198]:= NMaximize[{logLikelihood1[t1, t2, t3, t4, t5, t6, t7, t8, > t9, t10, t11, t12], t1 > 0, t2 > 0, t3 > 0, t4 > 0, t5 > 0, t6 > 0, > t7 > 0, t8 > 0, t9 > 0, t10 > 0, t11 > 0, t12 > 0, > t1 + t10 + t11 + t12 + t2 + t3 + t4 + t5 + t6 + t7 + t8 + t9 == > 1}, {t1, t2, t3, t4, t5, t6, t7, t8, t9, t10, t11, t12}] > > During evaluation of In[198]:= NMaximize::nrnum: The function value \ > 15.77293.14159 I is not a real number at \ > {t1,t10,t11,t12,t2,t3,t4,t5,t6,t7,<<2>>} = {0.490249,<<9>>,<<2>>}. \ > >> > > Out[198]= {13.2945, {t1 > 2.10942*10^15, t10 > 2.22045*10^16, > t11 > 2.22045*10^16, t12 > 2.22045*10^16, > t2 > 1.11022*10^16, t3 > 2.22045*10^16, t4 > 2.22045*10^16, > t5 > 6.93889*10^18, t6 > 2.22045*10^16, > t7 > 1.11022*10^16, t8 > 4.44089*10^16, t9 > 1.}} > [...]
Handling of constraints can be slightly tricky; sometimes the code will allow a small amount of slop so as not to chase it's metaphorical tail trying to satisfy them. Some tactics you might try include forcing a log of a negative to evaluate to something that is clearly undesirable, and maybe further constraining so that all variables are lessequal to 1. Other things you could try include adding penalties based on UnitStep of negative variables, and maybe play with Precision/AccuracyGoal (I found that these hurt more than they helped).
Here is code to do some of this.
myLog[t_?NumberQ /; t<=0] := 10^6 myLog[t_] := Log[t]
vec = {0.00001712341312000713,4.102725237468317*^6,3.7864902508468615*^6, 9.215772325326653*^7,0.000057161484895917856,0.000012892953334779516, 8.646320198720343*^6,5.877910295858781*^6,1.6837835562631724*^6, 5.648647024829866*^6,8.90597537441381*^6,1.9727284288726167*^6};
vars = Array[t,Length[vec]];
logLikelihood1[vars:{_?NumberQ..}] := myLog[vec.vars]
In[49]:= InputForm[NMaximize[{logLikelihood1[vars], Flatten[{Map[0<=#<=1&,vars], Total[vars]==1}]}, vars]]
Out[49]//InputForm= {9.76963022735483, {t[1] > 0., t[2] > 0., t[3] > 0., t[4] > 0., t[5] > 1., t[6] > 0., t[7] > 0., t[8] > 0., t[9] > 0., t[10] > 0., t[11] > 0., t[12] > 0.}}
Daniel Lichtblau Wolfram Research

