Question

我正在尝试解决优化问题。 optim函数中的输入参数有一些下限和上限。所以我在optim函数中定义它们的边界。 Hoewever，我在定义边界时遇到错误。没有边界，代码似乎正常工作。但是，我必须定义界限。我怎么能用optim函数做到这一点？

假设我有以下数据：

data<-structure(c(0.00615493340985163, -0.0183523033409178, -0.0239523785317557, 
0.0119069594508896, -0.0236738098553008, 0.00620766467803002, 
0, 0, -0.0135139156796791, -0.013333722176743, 0.0268476378564221, 
-0.0135139156796791, -0.013333722176743, 0.013333722176743, 0.00673412977392229, 
-0.00673412977392229, 0, -0.00668908444213101, 0.00668908444213101, 
0, -0.0199344999738199, -0.00655749308617948, -0.0384668116232195, 
0.0254794345985866, 0.0598193511101729, -0.072640216412876, 0.0192934699679488, 
0, 0.0330067654193866, -0.013333722176743, 0.013333722176743, 
-0.013333722176743, 0.013333722176743, -0.00668908444213101, 
0, 0.0134232142160533, -0.00673412977392229, 0.0481199603578747, 
1.11022302462516e-16, -0.00701767864273251, -0.0138893197432578, 
0.0138893197432578, 0.0140849533532424, 0.0215065370300215, 0.0294143507296346, 
-0.00743509745461479, 0.0224732181609882, 0.0152677229601242, 
0.0233477550538765, -0.0684689206901783, 0.00738022451518927, 
0.00743509745461468, 2.22044604925031e-16, -0.0074350974546149, 
0.0149258899398627, 0.0228150511812496, 0.0233477550538768, -0.0310107541714851, 
-1.11022302462516e-16, 0.0794022066375132, -0.00823059632776157, 
0.0248978480958935, -0.0166672517681319, 0.0422008655824283, 
0.0262027007594979, -0.0262027007594979, -0.00858384940446988, 
-0.0418476125057201, -0.0711716103097515, -0.0151520520636412, 
-0.00749079248524787, 2.22044604925031e-16, -0.0074350974546149, 
0.0377409411211125, 0.00772217442522283, -0.00772217442522272, 
0.0155044452037838, 0.0813409849048499, 0.0432973437531967, 0.0639495630685765, 
0.0582697202410881, -0.00995047290670414, -0.038840374472406, 
-0.0188687397097502, -0.018519293799869, 0.00921677698219231, 
0.00930251681767669, 0.0577091141821562, 0.00496286001552748, 
-0.0148152957266917, 0.0198029086178682, -0.0049876128911765, 
0.0251906130129864, 0.0258416144357064, 0.026527158190343, -0.00536202564051175, 
0.0381523627082095, 0.0224732181609883, 0.00569811427981221, 
0.00573076894503241, 0.0115610141605023, -3.99203730968607, -3.30187780145509, 
-3.50548223941826, -2.91752716824826, -3.17492763371365, -3.53507451548409, 
-3.89518141271414, -3.88152836923837, -3.8883781931234, -3.90193865793583, 
-3.62428166915146, -3.89518141271415, -4.31078411075375, -3.90865054602706, 
-3.61759188278133, -3.90865054602705, -3.89518141271415, -3.21205168392545, 
-3.62428166915146, -3.62428166915146, -3.90865054602706, -3.23199118204902, 
-3.42417422616045, -3.67624725795418, -3.25797324409979, -2.05477936938672, 
-3.25154075748913, -3.65707525404955, -3.23855027497075, -3.61759188278133, 
-3.63092699428175, -3.39105256160677, -3.62428166915146, -3.62428166915146, 
-3.4110569336503, -3.90865054602705, -3.61085703614421, -3.04773029538416, 
-3.34980147791793, -3.8606927748257, -3.58345463266905, -3.87463129809686, 
-3.58345463266904, -3.15684949369853, -3.54088930436154, -3.12806158534685, 
-3.51890725078025, -2.92522323350839, -3.48116118577917, -3.06787261524203, 
-2.9479621461587, -3.81031850036527, -3.28454665255894, -3.29201110603814, 
-3.51890725078025, -3.50397938330381, -3.08326299924448, -3.06008764562223, 
-3.09842002466534, -2.38191708519966, -3.40940510523282, -3.40940510523283, 
-2.70767965228382, -3.00382611773014, -2.35925234419376, -2.54283503639689, 
-2.34190966178995, -2.36781202087106, -2.43376975085178, -3.78035118847322, 
-3.5039793833038, -3.28454665255894, -2.69649797383879, -2.96283902618942, 
-2.79544487368831, -2.76441473522112, -2.32836109669588, -2.75650428162744, 
-2.82871191242858, -2.63863192436288, -2.52047288863833, -3.51147117607425, 
-3.52137370329194, -2.71243376070309, -3.98895546754183, -3.99817264464609, 
-3.07713524996792, -2.70290281739706, -3.36965724112176, -3.34980147791793, 
-3.0104186116689, -3.51147117607425, -2.72042800404975, -3.47601897065901, 
-2.75119564294736, -3.43926334778568, -3.13533665372873, -3.38992938439265, 
-4.07468451164413, -4.06900240301525, -3.77271689629009), .Dim = c(101L, 
2L), .Dimnames = list(NULL, c("data", "range")))

使用下面的代码，我想用optim函数解决一个优化问题：

solfun<-function(par,data) 
{
  data1<-data[,1];
  data2<-data[,2];

  n<-length(data1)
  LL<-1:n;
  sigs<-1:(n+1);
  z<-1:n;
  xd<-1:n;
  sigs[1]<-sqrt(mean(data1^2)) ;
  for(i in 2:(n+1)) {
    z[i-1]=data1[i-1]/sigs[i-1];
    xd[i-1]=(data2[i-1]-0.43-log(sigs[i-1]))/0.29
    sigs[i]=exp(par[1]/2+par[3]*log(sigs[i-1])+par[4]/2*xd[i-1]+par[2]/2*z[i-1])
  } ;
  for(i in 1:n) {
    LL[i] <- (-0.5*log(sqrt(2*pi)*0.29)-(data2[i]-0.43-log(sigs[i]))^2/(2*0.29^2))
  };
  return(sum(-LL)) ;
} 


fit1<-optim(par<-c(0.19413280,0.02130018, 0.97327246, 0.13672007),solfun,data=data, 
            method = "L-BFGS-B",lower=c(-10,-10, -1,-10),upper=c(10,10, 1,10))

但是，我收到以下错误：

> fit1<-optim(par<-c(0.19413280,0.02130018, 0.97327246, 0.13672007),solfun,data=data, 
+             method = "L-BFGS-B",lower=c(-10,-10, -1,-10),upper=c(10,10, 1,10))
Error in optim(par <- c(0.1941328, 0.02130018, 0.97327246, 0.13672007),  : 
  L-BFGS-B needs finite values of 'fn'

非常感谢。如果有任何帮助，我将非常高兴。

Answer 1

问题是L-BFGS-B方法（optim中处理边界的唯一多变量方法）需要函数值为有限数，因此函数不能返回{{1} }，NaN在你的函数真正返回的范围内。所以这是一个处理你的问题的肮脏技巧。您可以如下定义函数Inf，这只是对solfun1的一点修改。当solfun值不是有限时，solfun会返回一个大数solfun1（这个数字应该多大取决于你遇到的问题，在这个问题中我发现它很大足够了，你可以灵活地设置数字）。我添加了一些术语return(1000 + sum(par ^ 2))以防止优化过程陷入困境。 sum(par ^ 2)可以很好地处理您的问题。

此外，在这个例子中，我发现边界是无用的，因为带有边界且没有边界的solfun1实际上会返回非常相似的结果。

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1 个答案: