el0ps.solver.OaSolver

class el0ps.solver.OaSolver(optimizer_name='gurobi', relative_gap=1e-08, absolute_gap=0.0, time_limit=None, iter_limit=None, inner_iter_limit=None, inner_rel_tol=1e-08, verbose=False, keeptrace=False)

Outer approximation solver for L0-regularized problems.

The problem is expressed as

\[\textstyle\min_{\mathbf{x} \in \mathbb{R}^{n}} f(\mathbf{Ax}) + \lambda\|\mathbf{x}\|_0 + h(\mathbf{x})\]

where \(f\) is a el0ps.datafit.BaseDatafit function, \(\mathbf{A} \in \mathbb{R}^{m \times n}\) is a matrix, \(h\) is a el0ps.penalty.BasePenalty function, and \(\lambda\) is a positive scalar. This method is based on the work presented in “A unified approach to mixed-integer optimization problems with logical constraints” by D. Bertsimas et al. To use this solver, the optimizer specified in the optimizer_name parameter must be installed and accessible by pyomo which is the underlying library used to model the outer problem.

Parameters:

optimizer_name: str = “gurobi”

Mixed-Integer Programming optimizer to use in the outer step. Available options are “cplex”, “gurobi”, and “mosek”.

relative_gap: float, default=1e-8

Relative tolerance on the objective value.

absolute_gap: float, default=0.0

Absolute tolerance on the objective value.

time_limit: float, default=None

Limit in second on the solving time.

iter_limit: int, default=None

Limit on the number of outer-approximation steps performed.

inner_iter_limit: int, default=None

Maximum number of iterations for the inner steps optimization solver.

inner_rel_tol: float, default=1e-8

Relative tolerance on the objective value for the inner steps.

verbose: bool, default=False

Whether to toggle solver verbosity.

keeptrace: bool, default=False

Whether to store the solver trace.

__init__(optimizer_name='gurobi', relative_gap=1e-08, absolute_gap=0.0, time_limit=None, iter_limit=None, inner_iter_limit=None, inner_rel_tol=1e-08, verbose=False, keeptrace=False)

Methods

__init__([optimizer_name, relative_gap, ...])
add_cut(optim, model, z, f, g)
build_model()
can_continue()
initialize_inner_solver()
initialize_optimizer()
inner_solve(z)
outer_solve(optim, model)
print_footer()
print_header()
print_progress()
solve(datafit, penalty, A, lmbd[, x_init])	Solve an L0-regularized problem.
update_bounds(zk, vk, xk, fk)
update_trace()

Attributes

abs_gap
accept_jitclass	Return whether if the solver accepts a jitclass for the datafit and penalty function.
rel_gap
timer