ex_problem.h

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#include <ifopt/variable_set.h>

namespace ifopt {
using Eigen::Vector2d;


class ExVariables : public VariableSet {
public:
  // Every variable set has a name, here "var_set1". this allows the constraints
  // and costs to define values and Jacobians specifically w.r.t this variable set.
  ExVariables() : ExVariables("var_set1") {};
  ExVariables(const std::string& name) : VariableSet(2, name)
  {
    // the initial values where the NLP starts iterating from
    x0_ = 0.5;
    x1_ = 1.5;
  }

  // Here is where you can transform the Eigen::Vector into whatever
  // internal representation of your variables you have (here two doubles, but
  // can also be complex classes such as splines, etc..
  virtual void SetVariables(const VectorXd& x) override
  {
    x0_ = x(0);
    x1_ = x(1);
  };

  // Here is the reverse transformation from the internal representation to
  // to the Eigen::Vector
  virtual VectorXd GetValues() const override
  {
    return Vector2d(x0_, x1_);
  };

  // Each variable has an upper and lower bound set here
  VecBound GetBounds() const override
  {
    VecBound bounds(GetRows());
    bounds.at(0) = Bounds(-1.0, 1.0);
    bounds.at(1) = NoBound;
    return bounds;
  }

private:
  double x0_, x1_;
};


class ExConstraint : public ConstraintSet {
public:
  ExConstraint() : ExConstraint("constraint1") {}

  // This constraint set just contains 1 constraint, however generally
  // each set can contain multiple related constraints.
  ExConstraint(const std::string& name) : ConstraintSet(1, name) {}

  // The constraint value minus the constant value "1", moved to bounds.
  virtual VectorXd GetValues() const override
  {
    VectorXd g(GetRows());
    Vector2d x = GetVariables()->GetComponent("var_set1")->GetValues();
    g(0) = std::pow(x(0),2) + x(1);
    return g;
  };

  // The only constraint in this set is an equality constraint to 1.
  // Constant values should always be put into GetBounds(), not GetValues().
  // For inequality constraints (<,>), use Bounds(x, inf) or Bounds(-inf, x).
  VecBound GetBounds() const override
  {
    VecBound b(GetRows());
    b.at(0) = Bounds(1.0, 1.0);
    return b;
  }

  // This function should provides the derivative of the constraint set.
  // can also tell the solvers to approximate the derivatives by finite
  // differences and simply leave this function empty by setting the solver
  // option in e.g. ipopt_adapter.cc::SetOptions():
  // SetStringValue("jacobian_approximation", "finite-difference-values");
  void FillJacobianBlock (std::string var_set, Jacobian& jac_block) const override
  {
    // must fill only that submatrix of the overall Jacobian that relates
    // to this constraint and "var_set1". even if more constraints or variables
    // classes are added, this submatrix will always start at row 0 and column 0,
    // thereby being independent from the overall problem.
    if (var_set == "var_set1") {

      Vector2d x = GetVariables()->GetComponent("var_set1")->GetValues();

      jac_block.coeffRef(0, 0) = 2.0*x(0); // derivative of first constraint w.r.t x0
      jac_block.coeffRef(0, 1) = 1.0;      // derivative of first constraint w.r.t x1
    }
  }
};


class ExCost: public CostTerm {
public:
  ExCost() : ExCost("cost_term1") {}
  ExCost(const std::string& name) : CostTerm(name) {}

  virtual double GetCost() const override
  {
    Vector2d x = GetVariables()->GetComponent("var_set1")->GetValues();
    return -std::pow(x(1)-2,2);
  };

  void FillJacobianBlock (std::string var_set, Jacobian& jac) const override
  {
    if (var_set == "var_set1") {

      Vector2d x = GetVariables()->GetComponent("var_set1")->GetValues();

      jac.coeffRef(0, 0) = 0.0;             // derivative of cost w.r.t x0
      jac.coeffRef(0, 1) = -2.0*(x(1)-2.0); // derivative of cost w.r.t x1
    }
  }
};

} // namespace opt