least_absolute_deviations.h

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// ----------------------------------------------------------------------------
// -                        CloudViewer: www.cloudViewer.org                  -
// ----------------------------------------------------------------------------
// Copyright (c) 2018-2024 www.cloudViewer.org
// SPDX-License-Identifier: MIT
// ----------------------------------------------------------------------------
 
#pragma once
 
#include <Eigen/Core>
#include <Eigen/SparseCore>
 
#include "util/logging.h"
 
namespace colmap {
 
struct LeastAbsoluteDeviationsOptions {
    // Augmented Lagrangian parameter.
    double rho = 1.0;
 
    // Over-relaxation parameter, typical values are between 1.0 and 1.8.
    double alpha = 1.0;
 
    // Maximum solver iterations.
    int max_num_iterations = 1000;
 
    // Absolute and relative solution thresholds, as suggested by Boyd et al.
    double absolute_tolerance = 1e-4;
    double relative_tolerance = 1e-2;
};
 
// Least absolute deviations (LAD) fitting via ADMM by solving the problem:
//
//        min || A x - b ||_1
//
// The solution is returned in the vector x and the iterative solver is
// initialized with the given value. This implementation is based on the paper
// "Distributed Optimization and Statistical Learning via the Alternating
// Direction Method of Multipliers" by Boyd et al. and the Matlab implementation
// at https://web.stanford.edu/~boyd/papers/admm/least_abs_deviations/lad.html
bool SolveLeastAbsoluteDeviations(const LeastAbsoluteDeviationsOptions& options,
                                  const Eigen::SparseMatrix<double>& A,
                                  const Eigen::VectorXd& b,
                                  Eigen::VectorXd* x);
 
}  // namespace colmap