fraction_to_the_boundary_rule.hpp

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// Copyright (c) Sleipnir contributors
 
#pragma once
 
#include <Eigen/Core>
 
// See docs/algorithms.md#Works_cited for citation definitions
 
namespace slp {
 
/// Applies fraction-to-the-boundary rule to a variable and its iterate, then
/// returns a fraction of the iterate step size within (0, 1].
///
/// @tparam Scalar Scalar type.
/// @param x The variable.
/// @param p The iterate on the variable.
/// @param τ Fraction-to-the-boundary rule scaling factor within (0, 1].
/// @return Fraction of the iterate step size within (0, 1].
template <typename Scalar>
Scalar fraction_to_the_boundary_rule(
    const Eigen::Vector<Scalar, Eigen::Dynamic>& x,
    const Eigen::Vector<Scalar, Eigen::Dynamic>& p, Scalar τ) {
  // α = max(α ∈ (0, 1] : x + αp ≥ (1 − τ)x)
  //
  // where x and τ are positive.
  //
  // x + αp ≥ (1 − τ)x
  // x + αp ≥ x − τx
  // αp ≥ −τx
  //
  // If the inequality is false, p < 0 and α is too big. Find the largest value
  // of α that makes the inequality true.
  //
  // α = −τ/p x
  Scalar α(1);
  for (int i = 0; i < x.rows(); ++i) {
    if (α * p(i) < -τ * x(i)) {
      α = -τ / p(i) * x(i);
    }
  }
 
  return α;
}
 
}  // namespace slp