gradient_descent_linesearch()

template<typename X , typename FunctionEval , typename GradientEval , typename LinesearchEval , typename RandomStep , typename Terminator >

auto syten::GradientOpt::gradient_descent_linesearch	(	X	x,
		FunctionEval	func,
		GradientEval	grad,
		LinesearchEval	lin,
		RandomStep	rand,
		Terminator	terminate,
		Index	num_steps = 100,
		Index	ls_num_steps = 50,
		SRDef	ls_lower = 0,
		SRDef	ls_upper = 1
	)

Attempt at a gradient descent with linesearch.

Works very badly.

Template Parameters

X	domain type
FunctionEval	type of the function evaluation function, taking an X
GradientEval	type of the gradient evaluation function, taking a result of the function and its X
LinesearchEval	type of the linesearch evaluation function, taking a step size a, the current iteration point x and the gradient g and returning the value of f(x-a*g) and ‘f’(x-a*g)` (wrt a).
RandomStep	type of the random stepper to be enacted if nothing else works. Takes the step size (either 0 or NAN) point and the gradient.
Terminator	type of the termination condition, returning true if we should break out. Takes the step size, current function value and current gradient.

Parameters

x	initial value
func	object returning f(x) when given x
grad	object returning f'(x) when given f(x) and x
lin	object returning f(x-a*g) and f'(x-a*g) (wrt a) when given a, x and g
rand	object returning an updated random x when given x and g
terminate	object returning true if, given a step size alpha, the current function value and the current gradient, we should terminate early.
num_steps	maximal number if outer steps to take
ls_num_steps	number of steps to be done during the linesearch
ls_lower	lower end of the line search
ls_upper	upper end of the line search

References syten::isnan(), linesearch(), std::make_tuple(), and std::move().

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