Problem with NMaximize

*To*: mathgroup at smc.vnet.net*Subject*: [mg90024] Problem with NMaximize*From*: Ramiro Barrantes-Reynolds <rbarrant at uvm.edu>*Date*: Thu, 26 Jun 2008 04:46:08 -0400 (EDT)

Hello, I am trying to calculate the maximum likelihood of a logarithmic function over 17 parameters. I am using NMaximize and setting all the parameters to be over 0, and the sum of the a group of them (t's) to be equal to 1 (i.e. t1 + t2 + t3 + t4 + t5 + t6 + t7 + t8 + t9 + t10 + t11 + t12 == 1) (complete code at the end). My constraints would then be: l1 > 0, l2 > 0, l3 > 0, l4 > 0, 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 + t2 + t3 + t4 + t5 + t6 + t7 + t8 + t9 + t10 + t11 + t12 == 1 When I run NMaximize over my function I get: NMaximize::nrnum: "The function value 28.2245-6.28319I is not a real number at {a,l1,l2,l3,l4,t1,t10,t11,t12,t2,<<7>>} ={1.,2.,2.,<<6>>,0.0799689,<<7>>}." which is because the number inside the logarithm is negative. When I used EvaluationMonitor and looked at the iterations I saw that the first iteration was: In[189]:= data[[1, 1]] Out[189]= {1., {2., 2., 2., 2.}, {1.22125*10^-15, 0., -2.22045*10^-16, 0., -2.22045*10^-16, -2.22045*10^-16, -2.22045*10^-16, -1.11022*10^-16, 1., -2.22045*10^-16, 0., 0.}} As you can see there are several negative numbers, even though the constraints should enforce otherwise. The error I get I think is a consequence of that, In[188]:= data[[1, -1]] Out[188]= {1., {2., 2., 2., 2.}, {t1, 0.0799689, 0.0478029, 0.0263613, 0.0356839, 0.0720513, 0.066108, 0.0861263, 1., 0.0849883, 0.0498477, 0.000577809}} This input would lead to my function evaluating a negative logarithm. However, NMaximize shouldn't be evaluating any negative numbers in the parameters right? Any ideas? Thank you, Ramiro {res, data} = Reap[NMaximize[{logLikelihood[{{5, 5, 0, 0}, {3, 1, 0, 1}}, {33, 83, 11, 14}, S, a, {l1, l2, l3, l4}, {t1, t2, t3, t4, t5, t6, t7, t8, t9, t10, t11, t12}], l1 > 0, l2 > 0, l3 > 0, l4 > 0, 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 + t2 + t3 + t4 + t5 + t6 + t7 + t8 + t9 + t10 + t11 + t12 == 1}, {a, l1, l2, l3, l4, t1, t2, t3, t4, t5, t6, t7, t8, t9, t10, t11, t12}, EvaluationMonitor :> Sow[{a, {l1, l2, l3, l4}, {t1, t2, t3, t4, t5, t6, t7, t8, t9, t10, t11, t12}}]]]; NMaximize::nrnum: The function value 28.2245-6.28319 I is not a real \ number at {a,l1,l2,l3,l4,t1,t10,t11,t12,t2,<<7>>} = \ {1.,2.,2.,<<6>>,0.0799689,<<7>>}. >>