void ArmijoLineSearch::Search(const LineSearch::Options& options,
const double initial_step_size,
const double initial_cost,
const double initial_gradient,
Summary* summary) {
*CHECK_NOTNULL(summary) = LineSearch::Summary();
Function* function = options.function;
double previous_step_size = 0.0;
double previous_cost = 0.0;
double previous_gradient = 0.0;
bool previous_step_size_is_valid = false;
double step_size = initial_step_size;
double cost = 0.0;
double gradient = 0.0;
bool step_size_is_valid = false;
++summary->num_evaluations;
step_size_is_valid =
function->Evaluate(step_size,
&cost,
options.interpolation_degree < 2 ? NULL : &gradient);
while (!step_size_is_valid || cost > (initial_cost
+ options.sufficient_decrease
* initial_gradient
* step_size)) {
// If step_size_is_valid is not true we treat it as if the cost at
// that point is not large enough to satisfy the sufficient
// decrease condition.
const double current_step_size = step_size;
// Backtracking search. Each iteration of this loop finds a new point
if ((options.interpolation_degree == 0) || !step_size_is_valid) {
// Backtrack by halving the step_size;
step_size *= 0.5;
} else {
// Backtrack by interpolating the function and gradient values
// and minimizing the corresponding polynomial.
vector<FunctionSample> samples;
samples.push_back(ValueAndGradientSample(0.0,
initial_cost,
initial_gradient));
if (options.interpolation_degree == 1) {
// Two point interpolation using function values and the
// initial gradient.
samples.push_back(ValueSample(step_size, cost));
if (options.use_higher_degree_interpolation_when_possible &&
summary->num_evaluations > 1 &&
previous_step_size_is_valid) {
// Three point interpolation, using function values and the
// initial gradient.
samples.push_back(ValueSample(previous_step_size, previous_cost));
}
} else {
// Two point interpolation using the function values and the gradients.
samples.push_back(ValueAndGradientSample(step_size,
cost,
gradient));
if (options.use_higher_degree_interpolation_when_possible &&
summary->num_evaluations > 1 &&
previous_step_size_is_valid) {
// Three point interpolation using the function values and
// the gradients.
samples.push_back(ValueAndGradientSample(previous_step_size,
previous_cost,
previous_gradient));
}
}
double min_value;
MinimizeInterpolatingPolynomial(samples, 0.0, current_step_size,
&step_size, &min_value);
step_size =
min(max(step_size,
options.min_relative_step_size_change * current_step_size),
options.max_relative_step_size_change * current_step_size);
}
previous_step_size = current_step_size;
previous_cost = cost;
previous_gradient = gradient;
if (fabs(initial_gradient) * step_size < options.step_size_threshold) {
LOG(WARNING) << "Line search failed: step_size too small: " << step_size;
return;
}
++summary->num_evaluations;
step_size_is_valid =
function->Evaluate(step_size,
&cost,
options.interpolation_degree < 2 ? NULL : &gradient);
}
summary->optimal_step_size = step_size;
summary->success = true;
}
