data/DWSIM.Math/IPOPTSolver.vb

'    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