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Refactor interior-point method into separate file #245

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Dec 18, 2023
Merged

Refactor interior-point method into separate file #245

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109 changes: 6 additions & 103 deletions include/sleipnir/optimization/OptimizationProblem.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -3,15 +3,13 @@
#pragma once

#include <concepts>
#include <fstream>
#include <functional>
#include <optional>
#include <type_traits>
#include <utility>
#include <vector>

#include <Eigen/Core>
#include <Eigen/SparseCore>

#include "sleipnir/autodiff/Variable.hpp"
#include "sleipnir/autodiff/VariableMatrix.hpp"
Expand Down Expand Up @@ -372,124 +370,29 @@ class SLEIPNIR_DLLEXPORT OptimizationProblem {
// https://stackoverflow.com/a/50639754
static constexpr SolverConfig kDefaultConfig{};

// Decision variables, which are the root of the problem's expression tree
// The list of decision variables, which are the root of the problem's
// expression tree
std::vector<Variable> m_decisionVariables;

// Cost function: f(x)
// The cost function: f(x)
std::optional<Variable> m_f;

// Equality constraints: cₑ(x) = 0
// The list of equality constraints: cₑ(x) = 0
std::vector<Variable> m_equalityConstraints;

// Inequality constraints: cᵢ(x) ≥ 0
// The list of inequality constraints: cᵢ(x) ≥ 0
std::vector<Variable> m_inequalityConstraints;

SolverConfig m_config;

// Sparsity pattern files written when spy flag is set in SolverConfig
std::ofstream m_H_spy;
std::ofstream m_A_e_spy;
std::ofstream m_A_i_spy;

// The user callback
std::function<bool(const SolverIterationInfo&)> m_callback =
[](const SolverIterationInfo&) { return false; };

/**
Find the optimal solution to the nonlinear program using an interior-point
solver.

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] initialGuess The initial guess.
@param[out] status The solver status.
*/
Eigen::VectorXd InteriorPoint(
const Eigen::Ref<const Eigen::VectorXd>& initialGuess,
SolverStatus* status);

/**
* Prints exit condition as a user-readable message.
*
* @param exitCondition The solver exit condition.
*/
static void PrintExitCondition(const SolverExitCondition& exitCondition);

/**
* Returns true if the problem is locally feasible.
*
* @param A_e The problem's equality constraint Jacobian Aₑ(x) evaluated at
* the current iterate.
* @param c_e The problem's equality constraints cₑ(x) evaluated at the
* current iterate.
* @param A_i The problem's inequality constraint Jacobian Aᵢ(x) evaluated at
* the current iterate.
* @param c_i The problem's inequality constraints cᵢ(x) evaluated at the
* current iterate.
*/
bool IsLocallyFeasible(const Eigen::SparseMatrix<double>& A_e,
const Eigen::VectorXd& c_e,
const Eigen::SparseMatrix<double>& A_i,
const Eigen::VectorXd& c_i) const;

/**
* Returns the error estimate using the KKT conditions for the interior-point
* method.
*
* @param g Gradient of the cost function ∇f.
* @param A_e The problem's equality constraint Jacobian Aₑ(x) evaluated at
* the current iterate.
* @param c_e The problem's equality constraints cₑ(x) evaluated at the
* current iterate.
* @param A_i The problem's inequality constraint Jacobian Aᵢ(x) evaluated at
* the current iterate.
* @param c_i The problem's inequality constraints cᵢ(x) evaluated at the
* current iterate.
* @param s Inequality constraint slack variables.
* @param y Equality constraint dual variables.
* @param z Inequality constraint dual variables.
* @param μ Barrier parameter.
*/
double ErrorEstimate(const Eigen::VectorXd& g,
const Eigen::SparseMatrix<double>& A_e,
const Eigen::VectorXd& c_e,
const Eigen::SparseMatrix<double>& A_i,
const Eigen::VectorXd& c_i, const Eigen::VectorXd& s,
const Eigen::VectorXd& y, const Eigen::VectorXd& z,
double μ) const;

/**
* Returns the KKT error for the interior-point method.
*
* @param g Gradient of the cost function ∇f.
* @param A_e The problem's equality constraint Jacobian Aₑ(x) evaluated at
* the current iterate.
* @param c_e The problem's equality constraints cₑ(x) evaluated at the
* current iterate.
* @param A_i The problem's inequality constraint Jacobian Aᵢ(x) evaluated at
* the current iterate.
* @param c_i The problem's inequality constraints cᵢ(x) evaluated at the
* current iterate.
* @param s Inequality constraint slack variables.
* @param y Equality constraint dual variables.
* @param z Inequality constraint dual variables.
* @param μ Barrier parameter.
*/
double KKTError(const Eigen::VectorXd& g,
const Eigen::SparseMatrix<double>& A_e,
const Eigen::VectorXd& c_e,
const Eigen::SparseMatrix<double>& A_i,
const Eigen::VectorXd& c_i, const Eigen::VectorXd& s,
const Eigen::VectorXd& y, const Eigen::VectorXd& z,
double μ) const;
};

} // namespace sleipnir
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