When Nelder-Mead method is applied to a simple quadratic polynomial, the minimization is unable to identify the minimum. It is quite close, but the modification of StopCriterion or the NmConfig isn't trivial without further documentation.
Solution
Description of the fields in the documentation.
Steps to reproduce
#r "nuget: Plotly.NET"
#r "nuget: FSharp.Stats, 0.4.12-preview.2"
open FSharp.Stats
open FSharp.Stats.Optimization
open System
open Plotly.NET
let myFunction (xs: vector) =
let x = xs.[0]
x**2. - 0.32*x - 0.13
// initial guess for the optimization
let x0 = vector [| -0.3 |]
// default solver options
let nmc = NelderMead.NmConfig.defaultInit()
// optimization procedure
let optim =
//let stopCrit =
// { OptimizationStop.defaultStopCriteria with MinFunctionEpsilon = 1e-24 }
//NelderMead.minimizeWithStopCriteria nmc x0 myFunction stopCrit
NelderMead.minimize nmc x0 myFunction
(*
optim.Vectors just contains 3 valid vectors
*)
let validVectors = 3
// optimization results as x, y, and z coordinate
let xs,ys =
optim.Vectors.[0..validVectors - 1] |> Array.map (fun x -> x.[0],myFunction x)
|> Array.unzip
let optimizationPathchart =
[
[-1. .. 0.005 .. 1.] |> List.map (fun x -> x,myFunction (vector [x])) |> Chart.Line
Chart.Line(x=xs,y=ys,ShowMarkers=true,Name="Optimization path")
Chart.Point([optim.SolutionVector.[0],optim.Solution],Name="Solution")
]
|> Chart.combine
|> Chart.withTemplate ChartTemplates.lightMirrored
|> Chart.withXAxisStyle ("x",ShowGrid=false)
|> Chart.withYAxisStyle ("myFunction(x)",ShowGrid=false)
|> Chart.withSize (800.,800.)
Chart.show optimizationPathchart
The problem at the current state is the negative part of the objective function. If a step during the optimization hits a negative value, the procedure is stopped immediately. A fix for this is in preparation
Problem
When Nelder-Mead method is applied to a simple quadratic polynomial, the minimization is unable to identify the minimum. It is quite close, but the modification of
StopCriterion
or theNmConfig
isn't trivial without further documentation.Solution
Description of the fields in the documentation.
Steps to reproduce