regpy.solvers.nonlinear.fista¶
Classes¶
The generalized FISTA algorithm for minimization of Tikhonov functionals |
Module Contents¶
- class regpy.solvers.nonlinear.fista.FISTA(setting, init=None, tau=10**16, eta=0.8, op_lower_bound=0, proximal_pars=None, logging_level='INFO', data=None, without_codomain_vectors=False)[source]¶
Bases:
regpy.solvers.general.RegSolverThe generalized FISTA algorithm for minimization of Tikhonov functionals
\[\mathcal{S}_{g^{\delta}}(F(f)) + \alpha \mathcal{R}(f).\]Gradient steps are performed on the first term, and proximal steps on the second term. The step sizes for the gradient steps are determined using a backtracking method introduced in A. Beck and M. Teboulle. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci., 2(1):183–202, 2009.
- Parameters:
setting (regpy.solvers.Setting) – The setting of the forward problem. Includes the penalty and data fidelity functionals.
init (setting.op.domain [default: setting.op.domain.zeros()]) – The initial guess
tau (float [default: 10**16]) – Initial step size of minimization procedure. Has to be sufficiently large.
eta (float [default 0.8]) – Step size reduction constant.
op_lower_bound (float [default: 0]) – lower bound of the operator: \(\|op(f)\|\geq op_lower_bound * \|f\|\). Used to define convexity parameter of data functional.
proximal_pars (dict [default: {}]) – Parameter dictionary passed to the computation of the prox-operator for the penalty term.
logging_level ([default: logging.INFO]) – logging level
- x¶
The current iterate.
- data = None¶
- regpar¶
- mu_penalty¶
- mu_data_fidelity¶
- proximal_pars = None¶
Proximal parameters that are passed to prox-operator of penalty term.
- without_codomain_vectors = False¶
- eta = 0.8¶
- t = 0¶
- t_old = 0¶
- mu¶
- x_old¶
- q¶