affine_scalar_constraint.h

/*
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 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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 * Please contact the author(s) of this library if you have any questions.
 * Authors: David Fridovich-Keil   ( dfk@eecs.berkeley.edu )
 */

///////////////////////////////////////////////////////////////////////////////
//
// (Time-invariant) affine scalar constraint, i.e., g(x) = a^T x - b.
//
///////////////////////////////////////////////////////////////////////////////

#ifndef ILQGAMES_CONSTRAINT_AFFINE_SCALAR_CONSTRAINT_H
#define ILQGAMES_CONSTRAINT_AFFINE_SCALAR_CONSTRAINT_H

#include <ilqgames/constraint/time_invariant_constraint.h>
#include <ilqgames/utils/types.h>

#include <glog/logging.h>
#include <memory>
#include <string>

namespace ilqgames {

class AffineScalarConstraint : public TimeInvariantConstraint {
 public:
  ~AffineScalarConstraint() {}
  AffineScalarConstraint(const VectorXf& a, float b, bool is_equality,
                         const std::string& name = "")
      : TimeInvariantConstraint(is_equality, name),
        a_(a),
        b_(b),
        hess_of_sq_(a * a.transpose()) {}

  // Evaluate this constraint value, i.e., g(x).
  float Evaluate(const VectorXf& input) const {
    CHECK_EQ(a_.size(), input.size());
    return a_.transpose() * input - b_;
  }

  // Quadraticize the constraint value and its square, each scaled by lambda or
  // mu, respectively (terms in the augmented Lagrangian).
  void Quadraticize(Time t, const VectorXf& input, MatrixXf* hess,
                    VectorXf* grad) const {
    CHECK_NOTNULL(hess);
    CHECK_NOTNULL(grad);
    CHECK_EQ(input.size(), a_.size());
    CHECK_EQ(hess->rows(), input.size());
    CHECK_EQ(hess->cols(), input.size());
    CHECK_EQ(grad->size(), input.size());

    // Get current lambda and mu.
    const float lambda = Lambda(t);
    const float mu = Mu(t, input);

    // Compute gradient and Hessian.
    (*grad) += lambda * a_ + mu * (hess_of_sq_ * input - b_ * a_);
    (*hess) += mu * hess_of_sq_;
  }

 private:
  // Coefficient vector and nominal value.
  const VectorXf a_;
  const float b_;

  // Precompute Hessian of constraint squared (for speed).
  const MatrixXf hess_of_sq_;
};  //\class AffineScalarConstraint

}  // namespace ilqgames

#endif