Python package that implements an accelerated proximal gradient method for minimizing convex functions (Nesterov 2007, Beck and Teboulle 2009).
solves:
minimize f(x) + h(x)
over x \in R^dim_x
where f is smooth, convex - user supplies function to evaluate gradient of f
h is convex - user supplies function to evaluate the proximal operator of h
call as:
x = apgpy.solve( grad_f, prox_h, dim_x )
solve has call signature:
def solve(grad_f, prox_h, dim_x,
max_iters=2000,
eps=1e-6,
alpha=1.01,
beta=0.5,
gen_plots=True,
use_restart=True,
x_init=False,
quiet=False,
use_gra=False,
step_size=False,
fixed_step_size=False,
debug=False)
this takes in two functions:
grad_f(v) = df(v)/dv
(gradient of f at v)
prox_h(v, t) = argmin_x ( t * h(x) + 1/2 * norm(x-v)^2 )
where t is the (scalar, positive) step size at that iteration
each iteration of apg requires one gradient evaluation of f and one prox step with h
quits when:
norm( y(k) - x(k+1) ) / t < eps * max( 1,norm( x(k+1) )
apg implements something similar to TFOCS step-size adaptation (Becker, Candes and Grant 2010)
and gradient-scheme adaptive restarting (O'Donoghue and Candes 2013)
see notebooks/ for usage instances
to install type
python setup.py install