affine_vector_constraint.h

/*
 * Copyright (c) 2020, The Regents of the University of California (Regents).
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 *    2. Redistributions in binary form must reproduce the above
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 *       from this software without specific prior written permission.
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 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS
 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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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 vector constraint, i.e., g(x) = ||A x - b||.
//
///////////////////////////////////////////////////////////////////////////////

#ifndef ILQGAMES_CONSTRAINT_AFFINE_VECTOR_CONSTRAINT_H
#define ILQGAMES_CONSTRAINT_AFFINE_VECTOR_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 AffineVectorConstraint : public TimeInvariantConstraint {
 public:
  ~AffineVectorConstraint() {}
  AffineVectorConstraint(const MatrixXf& A, const VectorXf& b, bool is_equality,
                         const std::string& name = "")
      : TimeInvariantConstraint(is_equality, name),
        A_(A),
        b_(b),
        ATA_(A.transpose() * A),
        AAT_(A * A.transpose()) {
    CHECK_EQ(A_.rows(), b_.size());
  }

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

  // 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(), b_.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 value of the constraint.
    const VectorXf delta = A_ * input - b_;
    const float value = delta.norm();

    // Compute gradient and Hessian.
    const VectorXf AT_delta = A_.transpose() * delta;
    (*grad) += (mu + lambda / value) * AT_delta;
    (*hess) += (lambda / value) *
                   (AAT_ - AT_delta * AT_delta.transpose() / (value * value)) +
               mu * ATA_;
  }

 private:
  // A and b.
  const MatrixXf A_;
  const VectorXf b_;

  // Precompute ATA and AAT.
  const MatrixXf ATA_;
  const MatrixXf AAT_;
};  //\class AffineVectorConstraint

}  // namespace ilqgames

#endif