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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2012 Google Inc. All rights reserved.
// http://code.google.com/p/ceres-solver/
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
//
// * Redistributions of source code must retain the above copyright notice,
// this list of conditions and the following disclaimer.
// * Redistributions in binary form must reproduce the above copyright notice,
// this list of conditions and the following disclaimer in the documentation
// and/or other materials provided with the distribution.
// * Neither the name of Google Inc. nor the names of its contributors may be
// used to endorse or promote products derived from this software without
// specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
// POSSIBILITY OF SUCH DAMAGE.
//
// Author: sameeragarwal@google.com (Sameer Agarwal)
//
// Interface for and implementation of various Line search algorithms.
#ifndef CERES_INTERNAL_LINE_SEARCH_H_
#define CERES_INTERNAL_LINE_SEARCH_H_
#ifndef CERES_NO_LINE_SEARCH_MINIMIZER
#include <glog/logging.h>
#include <vector>
#include "ceres/internal/eigen.h"
#include "ceres/internal/port.h"
namespace ceres {
namespace internal {
class Evaluator;
// Line search is another name for a one dimensional optimization
// algorithm. The name "line search" comes from the fact one
// dimensional optimization problems that arise as subproblems of
// general multidimensional optimization problems.
//
// While finding the exact minimum of a one dimensionl function is
// hard, instances of LineSearch find a point that satisfies a
// sufficient decrease condition. Depending on the particular
// condition used, we get a variety of different line search
// algorithms, e.g., Armijo, Wolfe etc.
class LineSearch {
public:
class Function;
struct Options {
Options()
: interpolation_degree(1),
use_higher_degree_interpolation_when_possible(false),
sufficient_decrease(1e-4),
min_relative_step_size_change(1e-3),
max_relative_step_size_change(0.6),
step_size_threshold(1e-9),
function(NULL) {}
// TODO(sameeragarwal): Replace this with enums which are common
// across various line searches.
//
// Degree of the polynomial used to approximate the objective
// function. Valid values are {0, 1, 2}.
//
// For Armijo line search
//
// 0: Bisection based backtracking search.
// 1: Quadratic interpolation.
// 2: Cubic interpolation.
int interpolation_degree;
// Usually its possible to increase the degree of the
// interpolation polynomial by storing and using an extra point.
bool use_higher_degree_interpolation_when_possible;
// Armijo line search parameters.
// Solving the line search problem exactly is computationally
// prohibitive. Fortunately, line search based optimization
// algorithms can still guarantee convergence if instead of an
// exact solution, the line search algorithm returns a solution
// which decreases the value of the objective function
// sufficiently. More precisely, we are looking for a step_size
// s.t.
//
// f(step_size) <= f(0) + sufficient_decrease * f'(0) * step_size
double sufficient_decrease;
// In each iteration of the Armijo line search,
//
// new_step_size >= min_relative_step_size_change * step_size
double min_relative_step_size_change;
// In each iteration of the Armijo line search,
//
// new_step_size <= max_relative_step_size_change * step_size
double max_relative_step_size_change;
// If during the line search, the step_size falls below this
// value, it is truncated to zero.
double step_size_threshold;
// The one dimensional function that the line search algorithm
// minimizes.
Function* function;
};
// An object used by the line search to access the function values
// and gradient of the one dimensional function being optimized.
//
// In practice, this object will provide access to the objective
// function value and the directional derivative of the underlying
// optimization problem along a specific search direction.
//
// See LineSearchFunction for an example implementation.
class Function {
public:
virtual ~Function() {}
// Evaluate the line search objective
//
// f(x) = p(position + x * direction)
//
// Where, p is the objective function of the general optimization
// problem.
//
// g is the gradient f'(x) at x.
//
// f must not be null. The gradient is computed only if g is not null.
virtual bool Evaluate(double x, double* f, double* g) = 0;
};
// Result of the line search.
struct Summary {
Summary()
: success(false),
optimal_step_size(0.0),
num_evaluations(0) {}
bool success;
double optimal_step_size;
int num_evaluations;
};
virtual ~LineSearch() {}
// Perform the line search.
//
// initial_step_size must be a positive number.
//
// initial_cost and initial_gradient are the values and gradient of
// the function at zero.
// summary must not be null and will contain the result of the line
// search.
//
// Summary::success is true if a non-zero step size is found.
virtual void Search(const LineSearch::Options& options,
double initial_step_size,
double initial_cost,
double initial_gradient,
Summary* summary) = 0;
};
class LineSearchFunction : public LineSearch::Function {
public:
explicit LineSearchFunction(Evaluator* evaluator);
virtual ~LineSearchFunction() {}
void Init(const Vector& position, const Vector& direction);
virtual bool Evaluate(const double x, double* f, double* g);
private:
Evaluator* evaluator_;
Vector position_;
Vector direction_;
// evaluation_point = Evaluator::Plus(position_, x * direction_);
Vector evaluation_point_;
// scaled_direction = x * direction_;
Vector scaled_direction_;
Vector gradient_;
};
// Backtracking and interpolation based Armijo line search. This
// implementation is based on the Armijo line search that ships in the
// minFunc package by Mark Schmidt.
//
// For more details: http://www.di.ens.fr/~mschmidt/Software/minFunc.html
class ArmijoLineSearch : public LineSearch {
public:
virtual ~ArmijoLineSearch() {}
virtual void Search(const LineSearch::Options& options,
double initial_step_size,
double initial_cost,
double initial_gradient,
Summary* summary);
};
} // namespace internal
} // namespace ceres
#endif // CERES_NO_LINE_SEARCH_MINIMIZER
#endif // CERES_INTERNAL_LINE_SEARCH_H_
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