Parameters

The main interface for running the solver is run_solver() function. It takes the following arguments:

input_args: Input arguments for the solver.
solver_args: Solver arguments for the solver.
compute_args: Compute arguments for the solver.
objective_args: Objective arguments for the solver.
mlflow_config: MLflow configuration for the solver.

Input Arguments

The input arguments are displayed in the following table.

Input Arguments	Is Required	Default Value	Description
`A`	true	N/A	Tensor A.
`b`	true	N/A	Tensor b.
`C`	true	N/A	Tensor C.
`projection_maps`	true	N/A	Projection maps.

Solver Parameters

The solver settings are displayed in the following table.

Solevr Arguments	Is Required	Default Value	Description
`gamma`	false	1E-3	Ridge regularization parameter.
`max_iter`	false	10000	Maximum number of iterations.
`initial_step_size`	false	1e-5	Initial step size for the solver.
`max_step_size`	false	0.1	Upper bound for the solver’s step size.
`save_primal`	false	false	Flag to save primal variable values at the solution.
`initial_dual_path`	false	None	Filepath to initialize dual variables for algorithm restarts (optional).
`gamma_decay_type`	false	None	Type of gamma decay. We currently support “none” and “step”.
`gamma_decay_params`	false	None	Parameters for gamma decay. For “step” type gamme decay, “decay_steps” and “decay_rate” are the tunable parameters.
`decay_steps`	false	None	Number of steps before decaying gamma. This is only applicable when “step” type gamma decay is used.
`decay_rate`	false	None	Rate of gamma decay. This is only applicable when “step” type gamma decay is used.

Compute Parameters

The compute settings are displayed in the following table.

Compute Arguments	Is Required	Default Value	Description
`host_device`	true	N/A	Host device to compute the gradients. Choose from ‘cuda:0’ or ‘cpu’ with cuda:0 used when cuda is available.
`compute_device_num`	false	1	Number of compute devices to use for gradient computation.

The most efficient parameters are dependent on the problem scale and structure and there is no one-size-fits-all configuration. The default parameters usually can achieve acceptable performance, but users can definitely try tuning them if needed.

Objective Arguments

The objective arguments are displayed in the following table.

Objective Arguments	Is Required	Default Value	Description
`objective_type`	true	N/A	Type of objective function.
`objective_params`	false	None	Parameters for the objective function.

MLflow Configuration

The MLflow configuration is displayed in the following table.

MLflow Configuration	Is Required	Default Value	Description
`enabled`	true	N/A	Whether to enable MLflow logging.
`tracking_uri`	false	None	MLflow tracking URI.
`experiment_name`	false	None	MLflow experiment name.
`run_name`	false	None	MLflow run name.

The function run_solver() returns a SolverResult object.

SolverResult

The solver result is displayed in the following table.

Solver Result	Default Value	Description
`dual_val`	N/A	Dual variable value.
`dual_objective`	N/A	Dual objective value.
`objective_result`	N/A	The result of one gradient call.
`dual_objective_log`	N/A	Log of dual objective values.
`step_size_log`	N/A	Log of step sizes.

dual_objective_result is an object of the class ObjectiveResult and it contains the following attributes:

dual_gradient: Gradient of the dual objective function.
dual_objective: Dual objective value.
reg_penalty: Regularization penalty.
primal_objective: Primal objective value.
primal_var: Primal variable value.
dual_val_times_grad: Dual variable times gradient.
max_pos_slack: Maximum positive slack.
sum_pos_slack: Sum of positive slack.