In[]:=
logLMaxEnt[lambdas_]:=Module[{sum,logL,variances,penalty},​​sum=normData.lambdas;​​sum=sum-Max[sum];​​logL=Total[Take[sum,n]]/n-Log[Total[Exp[sum]]];​​variances=Variance[Take[normData,485]];​​penalty=Total[beta*Sqrt[variances/n]*Abs[lambdas]];​​logL-penalty​​]
In[]:=
AbsoluteTiming[FindMaximum[logLMaxEnt[{b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12}],Map[{#,0.}&,{b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12}],Method"Newton"]]
FindMaximum
:The line search decreased the step size to within the tolerance specified by AccuracyGoal and PrecisionGoal, but was unable to find a sufficient increase in the function. You may need more than MachinePrecision digits of working precision to meet these tolerances.
Out[]=
{1.31098,{-4.24499,{b113.7924,b22.63778,b310.0684,b41.93288,b54.09952,b60.622945,b7-9.29247,b88.84229,b9-16.6497,b10-3.5354×
-6
10
,b11-0.610985,b12-1.01583×
-8
10
}}}