cr.sparse.fom.fom¶
- cr.sparse.fom.fom(smooth_f, prox_h, A, b, x0, options=FomOptions(nonneg=False, solver='at', max_iters=1000, tol=1e-08, L0=1.0, Lexact=inf, alpha=0.9, beta=0.5, mu=0, maximize=False, saddle=False))[source]¶
First order methods driver routine
- Parameters
smooth_f (cr.sparse.opt.SmoothFunction) – A smooth function
prox_h (cr.sparse.opt.ProxCapable) – A prox-capable function
A (cr.sparse.lop.Operator) – A linear operator
b (jax.numpy.ndarray) – The translation vector
x0 (jax.numpy.ndarray) – Initial guess for solution vector
options (FomOptions) – Options for configuring the algorithm
- Returns
Solution of the optimization problem
- Return type
The function uses first order methods to solve an optimization problem of the form:
(1)¶\[\text{minimize } \phi(x) = f( \AAA(x) + b) + h(x)\]where:
\(\AAA\) is a linear operator from \(\RR^n \to \RR^m\).
\(b\) is a translation vector.
\(f : \RR^m \to \RR\) is a smooth convex function.
\(h : \RR^n \to \RR\) is a prox-capable convex function.
