interior_point.hpp

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// Copyright (c) Sleipnir contributors
 
#pragma once
 
#include <functional>
#include <span>
 
#include <Eigen/Core>
#include <Eigen/SparseCore>
 
#include "sleipnir/optimization/solver/exit_status.hpp"
#include "sleipnir/optimization/solver/iteration_info.hpp"
#include "sleipnir/optimization/solver/options.hpp"
#include "sleipnir/util/symbol_exports.hpp"
 
namespace slp {
 
/**
 * Matrix callbacks for the interior-point method solver.
 */
struct SLEIPNIR_DLLEXPORT InteriorPointMatrixCallbacks {
  /// Cost function value f(x) getter.
  ///
  /// <table>
  ///   <tr>
  ///     <th>Variable</th>
  ///     <th>Rows</th>
  ///     <th>Columns</th>
  ///   </tr>
  ///   <tr>
  ///     <td>x</td>
  ///     <td>num_decision_variables</td>
  ///     <td>1</td>
  ///   </tr>
  ///   <tr>
  ///     <td>f(x)</td>
  ///     <td>1</td>
  ///     <td>1</td>
  ///   </tr>
  /// </table>
  std::function<double(const Eigen::VectorXd& x)> f;
 
  /// Cost function gradient ∇f(x) getter.
  ///
  /// <table>
  ///   <tr>
  ///     <th>Variable</th>
  ///     <th>Rows</th>
  ///     <th>Columns</th>
  ///   </tr>
  ///   <tr>
  ///     <td>x</td>
  ///     <td>num_decision_variables</td>
  ///     <td>1</td>
  ///   </tr>
  ///   <tr>
  ///     <td>∇f(x)</td>
  ///     <td>num_decision_variables</td>
  ///     <td>1</td>
  ///   </tr>
  /// </table>
  std::function<Eigen::SparseVector<double>(const Eigen::VectorXd& x)> g;
 
  /// Lagrangian Hessian ∇ₓₓ²L(x, y, z) getter.
  ///
  /// L(xₖ, yₖ, zₖ) = f(xₖ) − yₖᵀcₑ(xₖ) − zₖᵀcᵢ(xₖ)
  ///
  /// <table>
  ///   <tr>
  ///     <th>Variable</th>
  ///     <th>Rows</th>
  ///     <th>Columns</th>
  ///   </tr>
  ///   <tr>
  ///     <td>x</td>
  ///     <td>num_decision_variables</td>
  ///     <td>1</td>
  ///   </tr>
  ///   <tr>
  ///     <td>y</td>
  ///     <td>num_equality_constraints</td>
  ///     <td>1</td>
  ///   </tr>
  ///   <tr>
  ///     <td>z</td>
  ///     <td>num_inequality_constraints</td>
  ///     <td>1</td>
  ///   </tr>
  ///   <tr>
  ///     <td>∇ₓₓ²L(x, y, z)</td>
  ///     <td>num_decision_variables</td>
  ///     <td>num_decision_variables</td>
  ///   </tr>
  /// </table>
  std::function<Eigen::SparseMatrix<double>(const Eigen::VectorXd& x,
                                            const Eigen::VectorXd& y,
                                            const Eigen::VectorXd& z)>
      H;
 
  /// Equality constraint value cₑ(x) getter.
  ///
  /// <table>
  ///   <tr>
  ///     <th>Variable</th>
  ///     <th>Rows</th>
  ///     <th>Columns</th>
  ///   </tr>
  ///   <tr>
  ///     <td>x</td>
  ///     <td>num_decision_variables</td>
  ///     <td>1</td>
  ///   </tr>
  ///   <tr>
  ///     <td>cₑ(x)</td>
  ///     <td>num_equality_constraints</td>
  ///     <td>1</td>
  ///   </tr>
  /// </table>
  std::function<Eigen::VectorXd(const Eigen::VectorXd& x)> c_e;
 
  /// Equality constraint Jacobian ∂cₑ/∂x getter.
  ///
  /// @verbatim
  ///         [∇ᵀcₑ₁(xₖ)]
  /// Aₑ(x) = [∇ᵀcₑ₂(xₖ)]
  ///         [    ⋮    ]
  ///         [∇ᵀcₑₘ(xₖ)]
  /// @endverbatim
  ///
  /// <table>
  ///   <tr>
  ///     <th>Variable</th>
  ///     <th>Rows</th>
  ///     <th>Columns</th>
  ///   </tr>
  ///   <tr>
  ///     <td>x</td>
  ///     <td>num_decision_variables</td>
  ///     <td>1</td>
  ///   </tr>
  ///   <tr>
  ///     <td>Aₑ(x)</td>
  ///     <td>num_equality_constraints</td>
  ///     <td>num_decision_variables</td>
  ///   </tr>
  /// </table>
  std::function<Eigen::SparseMatrix<double>(const Eigen::VectorXd& x)> A_e;
 
  /// Inequality constraint value cᵢ(x) getter.
  ///
  /// <table>
  ///   <tr>
  ///     <th>Variable</th>
  ///     <th>Rows</th>
  ///     <th>Columns</th>
  ///   </tr>
  ///   <tr>
  ///     <td>x</td>
  ///     <td>num_decision_variables</td>
  ///     <td>1</td>
  ///   </tr>
  ///   <tr>
  ///     <td>cᵢ(x)</td>
  ///     <td>num_inequality_constraints</td>
  ///     <td>1</td>
  ///   </tr>
  /// </table>
  std::function<Eigen::VectorXd(const Eigen::VectorXd& x)> c_i;
 
  /// Inequality constraint Jacobian ∂cᵢ/∂x getter.
  ///
  /// @verbatim
  ///         [∇ᵀcᵢ₁(xₖ)]
  /// Aᵢ(x) = [∇ᵀcᵢ₂(xₖ)]
  ///         [    ⋮    ]
  ///         [∇ᵀcᵢₘ(xₖ)]
  /// @endverbatim
  ///
  /// <table>
  ///   <tr>
  ///     <th>Variable</th>
  ///     <th>Rows</th>
  ///     <th>Columns</th>
  ///   </tr>
  ///   <tr>
  ///     <td>x</td>
  ///     <td>num_decision_variables</td>
  ///     <td>1</td>
  ///   </tr>
  ///   <tr>
  ///     <td>Aᵢ(x)</td>
  ///     <td>num_inequality_constraints</td>
  ///     <td>num_decision_variables</td>
  ///   </tr>
  /// </table>
  std::function<Eigen::SparseMatrix<double>(const Eigen::VectorXd& x)> A_i;
};
 
/**
Finds the optimal solution to a nonlinear program using the interior-point
method.
 
A nonlinear program has the form:
 
@verbatim
     min_x f(x)
subject to cₑ(x) = 0
           cᵢ(x) ≥ 0
@endverbatim
 
where f(x) is the cost function, cₑ(x) are the equality constraints, and cᵢ(x)
are the inequality constraints.
 
@param[in] matrix_callbacks Matrix callbacks.
@param[in] iteration_callbacks The list of callbacks to call at the beginning of
  each iteration.
@param[in] options Solver options.
@param[in,out] x The initial guess and output location for the decision
  variables.
@return The exit status.
*/
SLEIPNIR_DLLEXPORT ExitStatus
interior_point(const InteriorPointMatrixCallbacks& matrix_callbacks,
               std::span<std::function<bool(const IterationInfo& info)>>
                   iteration_callbacks,
               const Options& options,
#ifdef SLEIPNIR_ENABLE_BOUND_PROJECTION
               const Eigen::ArrayX<bool>& bound_constraint_mask,
#endif
               Eigen::VectorXd& x);
 
}  // namespace slp