steepest_descent_kernel.h File Reference

CUDA kernels of the steepest-descent optimizer. More...

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Functions
template<typename T >
__global__ void	sd_direction_kernel (T *__restrict__ s, const T *__restrict__ x, const T xmin, const T xmax, const int n)
template<typename T >
__global__ void	sd_update_move_limits_kernel (T *__restrict__ delta, const T *__restrict__ x, const T *__restrict__ x1, const T *__restrict__ x2, const T dec, const T inc, const T dmin, const T dmax, const int n)
template<typename T >
__global__ void	sd_update_design_kernel (T *__restrict__ x_new, const T *__restrict__ x, const T *__restrict__ s, const T *__restrict__ delta, const T psi, const T smax, const T xmin, const T xmax, const int n)

Detailed Description

Elementwise kernels of the steepest descent method with move limits, Appendix D of da Silva, Aage, Beck & Sigmund (2021), Eqs. D22-D24. They implement the same formulas as steepest_descent_cpu.f90.

Copyright

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Definition in file steepest_descent_kernel.h.

Function Documentation

sd_direction_kernel()

template<typename T >

__global__ void sd_direction_kernel	(	T *__restrict__	s,
		const T *__restrict__	x,
		const T	xmin,
		const T	xmax,
		const int	n
	)

Device kernel for the bound-projected steepest-descent direction (D22). On entry s holds the gradient G, on exit S = -G with every component that points out of the box at an active bound set to zero.

Parameters

s	Gradient on entry, projected direction on exit.
x	Design variables.
xmin	Lower bound of the design variables.
xmax	Upper bound of the design variables.
n	Number of design variables.

Definition at line 55 of file steepest_descent_kernel.h.

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sd_update_design_kernel()

template<typename T >

__global__ void sd_update_design_kernel	(	T *__restrict__	x_new,
		const T *__restrict__	x,
		const T *__restrict__	s,
		const T *__restrict__	delta,
		const T	psi,
		const T	smax,
		const T	xmin,
		const T	xmax,
		const int	n
	)

Device kernel for the move-limited, box-constrained update (D24). x_new = min(xmax, max(xmin, min(x + delta, max(x - delta, x + psi * (s / smax))))).

Parameters

x_new	Updated design variables.
x	Current design variables.
s	Bound-projected steepest-descent direction.
delta	Move limits.
psi	Step length.
smax	Global maximum of the absolute value of s.
xmin	Lower bound of the design variables.
xmax	Upper bound of the design variables.
n	Number of design variables.

Definition at line 122 of file steepest_descent_kernel.h.

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sd_update_move_limits_kernel()

template<typename T >

__global__ void sd_update_move_limits_kernel	(	T *__restrict__	delta,
		const T *__restrict__	x,
		const T *__restrict__	x1,
		const T *__restrict__	x2,
		const T	dec,
		const T	inc,
		const T	dmin,
		const T	dmax,
		const int	n
	)

Device kernel for the move-limit adaptation (D23). With d = (x - x1) * (x1 - x2), delta is scaled by dec where d < 0, by inc where d > 0, left unchanged where d = 0, and then clamped to [dmin, dmax].

Parameters

delta	Move limits, updated in place.
x	Design variables at the current iteration.
x1	Design variables one iteration back.
x2	Design variables two iterations back.
dec	Factor applied on oscillation.
inc	Factor applied on monotone progress.
dmin	Smallest allowed move limit.
dmax	Largest allowed move limit.
n	Number of design variables.

Definition at line 87 of file steepest_descent_kernel.h.

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