steepest_descent_math Module Reference

Vector-level kernels of the steepest-descent optimizer. More...

Functions/Subroutines
subroutine, public	sd_direction (s, x, xmin, xmax, n)
	Bound-projected steepest-descent direction (Eq. D22).
subroutine, public	sd_update_move_limits (delta, x, x1, x2, dec, inc, dmin, dmax, n)
	Adapt the move limits (Eq. D23).
subroutine, public	sd_update_design (x_new, x, s, delta, psi, smax, xmin, xmax, n)
	Move-limited, box-constrained design update (Eq. D24).

Detailed Description

Elementwise kernels of the steepest descent method with move limits, Appendix D of da Silva, Aage, Beck & Sigmund (2021), Eqs. D22-D24. Each routine operates on vector_t objects and runs on the device backend when one is configured, and on the CPU otherwise. All three are local operations; the global reduction of the direction is left to the caller.

Function/Subroutine Documentation

sd_direction()

subroutine, public steepest_descent_math::sd_direction	(	type(vector_t), intent(inout)	s,
		type(vector_t), intent(in)	x,
		real(kind=rp), intent(in)	xmin,
		real(kind=rp), intent(in)	xmax,
		integer, intent(in), optional	n
	)

On entry s holds the gradient G. On exit it holds S = -G, with S_e = 0 where x_e >= xmax and S_e > 0, or x_e <= xmin and S_e < 0.

Parameters

[in,out]	s	Gradient on entry, projected direction on exit.
[in]	x	Design variables.
[in]	xmin	Lower bound of the design variables.
[in]	xmax	Upper bound of the design variables.
[in]	n	Number of entries to process, the size of s by default.

Definition at line 65 of file steepest_descent_math.f90.

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sd_update_design()

subroutine, public steepest_descent_math::sd_update_design	(	type(vector_t), intent(inout)	x_new,
		type(vector_t), intent(in)	x,
		type(vector_t), intent(in)	s,
		type(vector_t), intent(in)	delta,
		real(kind=rp), intent(in)	psi,
		real(kind=rp), intent(in)	smax,
		real(kind=rp), intent(in)	xmin,
		real(kind=rp), intent(in)	xmax,
		integer, intent(in), optional	n
	)

Computes x_new = min(xmax, max(xmin, min(x + delta, max(x - delta, x + psi * (s / smax))))). This equals Eq. D24 whenever x lies in [xmin, xmax], and stays well defined for infeasible x.

Parameters

[in,out]	x_new	Updated design variables.
[in]	x	Current design variables.
[in]	s	Bound-projected steepest-descent direction.
[in]	delta	Move limits.
[in]	psi	Step length.
[in]	smax	Global maximum of the absolute value of s, which must be positive.
[in]	xmin	Lower bound of the design variables.
[in]	xmax	Upper bound of the design variables.
[in]	n	Number of entries to process, the size of x_new by default.

Definition at line 145 of file steepest_descent_math.f90.

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sd_update_move_limits()

subroutine, public steepest_descent_math::sd_update_move_limits	(	type(vector_t), intent(inout)	delta,
		type(vector_t), intent(in)	x,
		type(vector_t), intent(in)	x1,
		type(vector_t), intent(in)	x2,
		real(kind=rp), intent(in)	dec,
		real(kind=rp), intent(in)	inc,
		real(kind=rp), intent(in)	dmin,
		real(kind=rp), intent(in)	dmax,
		integer, intent(in), optional	n
	)

With d_e = (x_e - x1_e) * (x1_e - x2_e), the move limit is scaled by dec where d_e < 0, by inc where d_e > 0, left unchanged where d_e = 0, and then clamped to [dmin, dmax].

Parameters

[in,out]	delta	Move limits.
[in]	x	Design variables at the current iteration.
[in]	x1	Design variables one iteration back.
[in]	x2	Design variables two iterations back.
[in]	dec	Factor applied on oscillation.
[in]	inc	Factor applied on monotone progress.
[in]	dmin	Smallest allowed move limit.
[in]	dmax	Largest allowed move limit.
[in]	n	Number of entries to process, the size of delta by default.

Definition at line 103 of file steepest_descent_math.f90.

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