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gc_pwl_vb.vb
' Copyright 2024, Gurobi Optimization, LLC ' ' This example formulates and solves the following simple model ' with PWL constraints: ' ' maximize ' sum c[j] * x[j] ' subject to ' sum A[i,j] * x[j] <= 0, for i = 0, ..., m-1 ' sum y[j] <= 3 ' y[j] = pwl(x[j]), for j = 0, ..., n-1 ' x[j] free, y[j] >= 0, for j = 0, ..., n-1 ' where pwl(x) = 0, if x = 0 ' = 1+|x|, if x != 0 ' ' Note ' 1. sum pwl(x[j]) <= b is to bound x vector and also to favor sparse x vector. ' Here b = 3 means that at most two x[j] can be nonzero and if two, then ' sum x[j] <= 1 ' 2. pwl(x) jumps from 1 to 0 and from 0 to 1, if x moves from negatie 0 to 0, ' then to positive 0, so we need three points at x = 0. x has infinite bounds ' on both sides, the piece defined with two points (-1, 2) and (0, 1) can ' extend x to -infinite. Overall we can use five points (-1, 2), (0, 1), ' (0, 0), (0, 1) and (1, 2) to define y = pwl(x) Imports System Imports Gurobi Class gc_pwl_vb Shared Sub Main() Try Dim n As Integer = 5 Dim m As Integer = 5 Dim c As Double() = New Double() {0.5, 0.8, 0.5, 0.1, -1} Dim A As Double(,) = New Double(,) {{0, 0, 0, 1, -1}, _ {0, 0, 1, 1, -1}, _ {1, 1, 0, 0, -1}, _ {1, 0, 1, 0, -1}, _ {1, 0, 0, 1, -1}} Dim xpts As Double() = New Double() {-1, 0, 0, 0, 1} Dim ypts As Double() = New Double() {2, 1, 0, 1, 2} ' Env and model Dim env As GRBEnv = New GRBEnv() Dim model As GRBModel = New GRBModel(env) model.ModelName = "gc_pwl_cs" ' Add variables, set bounds and obj coefficients Dim x As GRBVar() = model.AddVars(n, GRB.CONTINUOUS) For i As Integer = 0 To n - 1 x(i).LB = -GRB.INFINITY x(i).Obj = c(i) Next Dim y As GRBVar() = model.AddVars(n, GRB.CONTINUOUS) ' Set objective to maximize model.ModelSense = GRB.MAXIMIZE ' Add linear constraints For i As Integer = 0 To m - 1 Dim le As GRBLinExpr = 0.0 For j As Integer = 0 To n - 1 le.AddTerm(A(i, j), x(j)) Next model.AddConstr(le, GRB.LESS_EQUAL, 0, "cx" & i) Next Dim le1 As GRBLinExpr = 0.0 For j As Integer = 0 To n - 1 le1.AddTerm(1.0, y(j)) Next model.AddConstr(le1, GRB.LESS_EQUAL, 3, "cy") ' Add piecewise constraints For j As Integer = 0 To n - 1 model.AddGenConstrPWL(x(j), y(j), xpts, ypts, "pwl" & j) Next ' Optimize model model.Optimize() For j As Integer = 0 To n - 1 Console.WriteLine("x[" & j & "] = " & x(j).X) Next Console.WriteLine("Obj: " & model.ObjVal) ' Dispose of model and environment model.Dispose() env.Dispose() Catch e As GRBException Console.WriteLine("Error code: " & e.ErrorCode & ". " & e.Message) End Try End Sub End Class