Added working box example

Author: kwesiRutledge

algorithms/tableau/selection/blands_rule.go

@@ -99,6 +99,8 @@ func (br BlandsRule) SelectEnteringAndExitingVariables(tableau utils.Tableau) (i
 		return -1, -1, nil // Optimal solution found, no entering variable
 	}
 
+	fmt.Println("Entering variable index:", enteringVarIdx)
+
 	// Select the exiting variable
 	exitingVarIdx := br.SelectExitingVariable(tableau, enteringVarIdx)
 	if exitingVarIdx == -1 {

examples/box1/box.go

@@ -0,0 +1,82 @@
+package main
+
+import (
+	"github.com/MatProGo-dev/MatProInterface.go/problem"
+	getKVector "github.com/MatProGo-dev/SymbolicMath.go/get/KVector"
+	"github.com/MatProGo-dev/SymbolicMath.go/symbolic"
+	"github.com/MatProGo-dev/simplex/simplexSolver"
+)
+
+/*
+Description:
+
+	This function builds an optimization problem where we attempt to find
+	the optimal solution to a linear programming problem that is in a feasible
+	region that is a box.
+
+	The problem will be:
+
+	Minimize:  x1 + 2*x2
+	Subject to:
+		0 <= x1 <= 1
+		0 <= x2 <= 1
+
+	The optimal solution is x1 = 0, x2 = 0 with an objective value of 0.
+*/
+func BuildOptimizationProblem() problem.OptimizationProblem {
+	// setup
+	varCount := 2
+	out := problem.NewProblem("Box LP Problem")
+
+	// Create the variables
+	x := out.AddVariableVector(varCount)
+
+	// Create the objective
+	c := getKVector.From(
+		[]float64{1, 2},
+	)
+	out.SetObjective(
+		c.Transpose().Multiply(x),
+		problem.SenseMinimize,
+	)
+
+	// Create the constraints
+	// - x >= 0
+	out.Constraints = append(
+		out.Constraints,
+		x.GreaterEq(symbolic.ZerosVector(varCount)),
+	)
+
+	// - x <= 1
+	out.Constraints = append(
+		out.Constraints,
+		x.LessEq(symbolic.OnesVector(varCount)),
+	)
+
+	return *out
+}
+
+func main() {
+	// This is just a placeholder to make the package "main" valid.
+	trickyProblem := BuildOptimizationProblem()
+
+	// Use solver to solve the problem
+	solver := simplexSolver.New("Simplex Solver Example")
+	solver.IterationLimit = 100
+
+	// Solve the problem
+	solution, err := solver.Solve(trickyProblem)
+	if err != nil {
+		panic(err)
+	}
+
+	// Print the solution
+	solutionMessage, _ := solution.Status.ToMessage()
+	println("Solution Status: ", solutionMessage)
+	println("Objective Value: ", solution.Objective)
+	println("Number of Iterations: ", solution.Iterations)
+	println("Variable Values: ")
+	for varName, varValue := range solution.VariableValues {
+		println("  ", varName, ": ", varValue)
+	}
+}