优化错误：框约束优化 (Julia Optim.jl)答案

【问题标题】：Optimization Error: Box constraint optimization (Julia Optim.jl)优化错误：框约束优化 (Julia Optim.jl)
【发布时间】：2019-12-31 16:51:59
【问题描述】：

我正在尝试运行以下代码 sn-p 来拟合一些经验数据的曲线，但是 Julia Optim.jl 包中的 optimize() 方法一直存在问题。我正在使用 Julia v1.1.0 并安装了所有正确的软件包。我不断收到的错误是：

ERROR: LoadError: MethodError: no method matching optimize(::getfield(Main, Symbol("##13#14")), ::Array{Float64,1}, ::Array{Int32,1}, ::Array{Float64,1}, ::Fminbox{LBFGS{Nothing,LineSearches.InitialStatic{Float64},LineSearches.HagerZhang{Float64,Base.RefValue{Bool}},getfield(Optim, Symbol("##19#21"))},Float64,getfield(Optim, Symbol("##43#45"))})

这是我的代码：

# Loading in dependencies
using Distributions # To use probability & statistics library
using Plots # To visualize results
using Optim # For minimization (curve fitting)

# Empirical data for curve fitting
IM = [1, 2, 3, 4] # x axis variables
pfs = [0.0, 0.0, 0.13, 0.23] # associated probabilities y-axis
n = 1000 # assume this number of independent trials for each x value

# Create functions to evaluate fit between theoretical values and empirical values
theor_vals = x -> cdf.(LogNormal(log(x[1]), x[2]), IM) # Assume lognormal shape and construct CDF with arbitrary fit parameters
likelihood = x -> [pdf(Binomial(n,xx[1]), round(xx[2])) for xx in zip(theor_vals(x),n.*pfs)] # getting likelihood values from binomial distribution for n trials
log_likelihood = x -> log.([xi > 0 ? xi : 1e-30 for xi in likelihood(x)]) # getting log value of likelihood
min_function = x -> -sum(log_likelihood(x)) # summing and switching sign for optimization


# Set inputs for minimization - first index is for the median and second index is for the dispersion (uncertainty)
init_guess = [median(IM), 0.5] # reasonable initial guess
lx = [0.001, 5.0] # lower bound
ux = [5,10] # upper bound

# Using Optim to optimize the objective function and get best curve fit
result = optimize(min_function, lx, ux, init_guess, Fminbox(LBFGS())) # call optimize function
theta, beta_a = result.minimizer # retrieve lognormal fit params

我还在熟悉 julia 语言，所以很可能我只是没有正确理解文档。提前感谢您提供的任何帮助或指导！

【问题讨论】：

LBFGS 来自哪里？
如果您将所有匿名函数改为常规命名函数，则错误消息可能会让您更好地指示哪个函数引发了方法错误。
另外，错误信息的其余部分是什么？

标签： optimization runtime-error julia mathematical-optimization

【解决方案1】：

你必须在你的代码中修复两件事，一切都会奏效：

ux 必须包含浮点数，因此您应该将其定义更改为 ux = [5.0,10.0]
init_guess 必须在优化范围内，以便您可以例如将其设置为init_guess = (lx+ux)/2

鉴于这些更改，您可以运行您的代码。这是我得到的结果（我没有从优化规范方面检查您的问题 - 我认为它是正确的；我只是提出了使您的示例可运行的更改）：

julia> result = optimize(min_function, lx, ux, init_guess, Fminbox(LBFGS()))
 * Status: success

 * Candidate solution
    Minimizer: [5.00e+00, 5.00e+00]
    Minimum:   1.417223e+03

 * Found with
    Algorithm:     Fminbox with L-BFGS
    Initial Point: [2.50e+00, 7.50e+00]

 * Convergence measures
    |x - x'|               = 8.88e-16 ≰ 0.0e+00
    |x - x'|/|x'|          = 1.26e-16 ≰ 0.0e+00
    |f(x) - f(x')|         = 0.00e+00 ≤ 0.0e+00
    |f(x) - f(x')|/|f(x')| = 0.00e+00 ≤ 0.0e+00
    |g(x)|                 = 8.87e+01 ≰ 1.0e-08

 * Work counters
    Seconds run:   0  (vs limit Inf)
    Iterations:    6
    f(x) calls:    2571
    ∇f(x) calls:   2571

【讨论】：