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' Copyright 2020 Daniel Wagner O. de Medeiros
'
' This file is part of DWSIM.
'
' DWSIM is free software: you can redistribute it and/or modify
' it under the terms of the GNU General Public License as published by
' the Free Software Foundation, either version 3 of the License, or
' (at your option) any later version.
'
' DWSIM is distributed in the hope that it will be useful,
' but WITHOUT ANY WARRANTY; without even the implied warranty of
' MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
' GNU General Public License for more details.
'
' You should have received a copy of the GNU General Public License
' along with DWSIM. If not, see <http://www.gnu.org/licenses/>.
Imports Cureos.Numerics
Namespace MathEx.Optimization
Public Class IPOPTSolver
Public Property Tolerance As Double = 0.0001
Public Property MaxIterations As Integer = 1000
Public Property ReturnLowestObjFuncValue As Boolean = True
Private _Iterations As Integer = 0
Private fxb As Func(Of Double(), Double)
Private fxg As Func(Of Double(), Double())
Private _error As Double
Private objval, objval0 As Double
Private Solutions As List(Of Double())
Private FunctionValues As List(Of Double)
Private Shared Lock As New Object
Public ReadOnly Property Iterations As Integer
Get
Return _Iterations
End Get
End Property
Sub New()
End Sub
Public Shared Function FindRoots(functionbody As Func(Of Double(), Double), vars As Double(), maxits As Integer, tol As Double,
Optional lbounds As Double() = Nothing, Optional ubounds As Double() = Nothing) As Double()
Dim ipopt As New IPOPTSolver
ipopt.Tolerance = tol
ipopt.MaxIterations = maxits
Return ipopt.Solve(functionbody, Nothing, vars, lbounds, ubounds)
End Function
''' <summary>
''' Minimizes a function value using IPOPT solver.
''' </summary>
''' <param name="functionbody">f(x) where x is a vector of doubles, returns the value of the function.</param>
''' <param name="functiongradient">Optional. g(x) where x is a vector of doubles, returns the value of the gradient of the function with respect to each variable.</param>
''' <param name="vars">initial values for x</param>
''' <param name="lbounds">lower bounds for x</param>
''' <param name="ubounds">upper bounds for x</param>
''' <returns>vector of variables corresponding to the function's minimum value.</returns>
Public Function Solve(functionbody As Func(Of Double(), Double), functiongradient As Func(Of Double(), Double()), vars As Double(), Optional lbounds As Double() = Nothing, Optional ubounds As Double() = Nothing) As Double()
_Iterations = 0
Dim obj As Double = 0.0#
Dim status As IpoptReturnCode = IpoptReturnCode.Feasible_Point_Found
Solutions = New List(Of Double())
FunctionValues = New List(Of Double)
fxb = functionbody
fxg = functiongradient
If lbounds Is Nothing Then
lbounds = vars.Clone()
For i As Integer = 0 To lbounds.Length - 1
lbounds(i) = -1.0E+19
Next
End If
If ubounds Is Nothing Then
ubounds = vars.Clone()
For i As Integer = 0 To ubounds.Length - 1
ubounds(i) = 1.0E+19
Next
End If
SyncLock Lock
Using problem As New Ipopt(vars.Length, lbounds, ubounds, 0, Nothing, Nothing,
0, 0, AddressOf eval_f, AddressOf eval_g,
AddressOf eval_grad_f, AddressOf eval_jac_g, AddressOf eval_h)
problem.AddOption("tol", Tolerance)
problem.AddOption("print_level", 0)
problem.AddOption("max_iter", MaxIterations)
problem.AddOption("mu_strategy", "adaptive")
problem.AddOption("hessian_approximation", "limited-memory")
'problem.AddOption("expect_infeasible_problem", "yes")
problem.SetIntermediateCallback(AddressOf intermediate)
status = problem.SolveProblem(vars, obj, Nothing, Nothing, Nothing, Nothing)
Select Case status
Case IpoptReturnCode.Solve_Succeeded,
IpoptReturnCode.Solved_To_Acceptable_Level,
IpoptReturnCode.Restoration_Failed,
IpoptReturnCode.Feasible_Point_Found,
IpoptReturnCode.Search_Direction_Becomes_Too_Small,
IpoptReturnCode.Infeasible_Problem_Detected,
IpoptReturnCode.Maximum_Iterations_Exceeded,
IpoptReturnCode.User_Requested_Stop
If ReturnLowestObjFuncValue Then
'get solution with lowest function value
Return Solutions(FunctionValues.IndexOf(FunctionValues.Min))
Else
Return vars
End If
Case Else
Throw New ArithmeticException("IPOPT failed to converge.")
End Select
End Using
End SyncLock
End Function
Private Function FunctionGradient(ByVal x() As Double) As Double()
Dim epsilon As Double = 0.001
Dim f1, f2 As Double
Dim g(x.Length - 1), x1(x.Length - 1), x2(x.Length - 1) As Double
Dim j, k As Integer
For j = 0 To x.Length - 1
For k = 0 To x.Length - 1
x1(k) = x(k)
x2(k) = x(k)
Next
If x(j) <> 0.0# Then
x1(j) = x(j) * (1.0# + epsilon)
x2(j) = x(j) * (1.0# - epsilon)
Else
x1(j) = x(j) + epsilon
x2(j) = x(j) - epsilon
End If
f1 = fxb.Invoke(x1)
f2 = fxb.Invoke(x2)
g(j) = (f2 - f1) / (x2(j) - x1(j))
Next
Return g
End Function
'IPOPT
Private Function eval_f(ByVal n As Integer, ByVal x As Double(), ByVal new_x As Boolean, ByRef obj_value As Double) As Boolean
Dim fval As Double = fxb.Invoke(x)
Solutions.Add(x)
FunctionValues.Add(fval)
obj_value = fval
Return True
End Function
Private Function eval_grad_f(ByVal n As Integer, ByVal x As Double(), ByVal new_x As Boolean, ByRef grad_f As Double()) As Boolean
Dim g As Double()
If fxg IsNot Nothing Then
g = fxg.Invoke(x)
Else
g = FunctionGradient(x)
End If
grad_f = g
Return True
End Function
Private Function eval_g(ByVal n As Integer, ByVal x As Double(), ByVal new_x As Boolean, ByVal m As Integer, ByRef g As Double()) As Boolean
Return True
End Function
Private Function eval_jac_g(ByVal n As Integer, ByVal x As Double(), ByVal new_x As Boolean, ByVal m As Integer, ByVal nele_jac As Integer, ByRef iRow As Integer(),
ByRef jCol As Integer(), ByRef values As Double()) As Boolean
Return False
End Function
Private Function eval_h(ByVal n As Integer, ByVal x As Double(), ByVal new_x As Boolean, ByVal obj_factor As Double, ByVal m As Integer, ByVal lambda As Double(),
ByVal new_lambda As Boolean, ByVal nele_hess As Integer, ByRef iRow As Integer(), ByRef jCol As Integer(), ByRef values As Double()) As Boolean
Return False
End Function
Private Function intermediate(ByVal alg_mod As IpoptAlgorithmMode, ByVal iter_count As Integer, ByVal obj_value As Double,
ByVal inf_pr As Double, ByVal inf_du As Double, ByVal mu As Double,
ByVal d_norm As Double, ByVal regularization_size As Double, ByVal alpha_du As Double,
ByVal alpha_pr As Double, ByVal ls_trials As Integer) As Boolean
_Iterations += 1
objval0 = objval
objval = obj_value
If Math.Abs(objval - objval0) <= Tolerance / 1000.0 And _Iterations > MaxIterations / 2 Then
Return False
Else
Return True
End If
End Function
End Class
End Namespace
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