CuPDLPx.jl

CuPDLPx.jl is a wrapper for the cuPDLPx solver.

It has two components:

• a thin wrapper around the complete C API
• an interface to MathOptInterface

Getting help

If you need help, please ask a question on the JuMP community forum.

If you have a reproducible example of a bug, please open a GitHub issue.

License

CuPDLPx.jl is licensed under the Apache 2.0 license.

The underlying solver, MIT-Lu-Lab/cuPDLPx, is licensed under the Apache 2.0 license.

Installation

Install CuPDLPx as follows:

import Pkg
Pkg.add("CuPDLPx")

In addition to installing the CuPDLPx.jl package, this will also download and install the cuPDLPx binaries. You do not need to install cuPDLPx separately.

Use with JuMP

To use CuPDLPx with JuMP, use CuPDLPx.Optimizer:

using JuMP, CuPDLPx
model = Model(CuPDLPx.Optimizer)
set_attribute(model, "verbose", true)
set_attribute(model, "l_inf_ruiz_iterations", 0)
set_attribute(model, "iteration_limit", 200)

Supported parameters

All of the following attributes are supported.

1. Termination criteria

Name	Type	Default	Description
eps_optimal_relative	Float64	1e-4	Relative tolerance for optimality gap.
eps_feasible_relative	Float64	1e-4	Relative tolerance for primal and dual feasibility.
eps_feas_polish_relative	Float64	1e-6	Relative tolerance used during the polishing phase.
time_sec_limit	Float64	3600.0	Maximum runtime allowed in seconds.
iteration_limit	Int32	2147483647	Maximum number of iterations.
optimality_norm	norm_type_t	NORM_TYPE_L2	Norm used to measure residuals: NORM_TYPE_L2 (0) or NORM_TYPE_L_INF (1).
termination_evaluation_frequency	Int	200	Frequency (in iterations) at which to check termination criteria.

2. Algorithm and Preconditioning

Name	Type	Default	Description
presolve	Bool	true	Whether to enable the PSLP presolver.
l_inf_ruiz_iterations	Int	10	Number of Ruiz rescaling iterations.
has_pock_chambolle_alpha	Bool	true	Whether to use Pock-Chambolle rescaling.
pock_chambolle_alpha	Float64	1.0	$\alpha$ used in Pock-Chambolle rescaling.
bound_objective_rescaling	Bool	true	Whether to use objective and bound rescaling.
reflection_coefficient	Float64	1.0	Reflection coefficient (typically in $[0, 1]$).
feasibility_polishing	Bool	false	Whether to perform post-solve feasibility polishing.
sv_max_iter	Int	5000	Maximum iterations for singular value estimation.
sv_tol	Float64	1e-4	Tolerance for singular value estimation.
verbose	Bool	false	Whether to enable console output and progress logging.

3. Adaptive Restart and Primal Weight

Name	Type	Default	Description
artificial_restart_threshold	Float64	0.36	Threshold for triggering a forced "artificial" restart (based on iterations).
sufficient_reduction_for_restart	Float64	0.2	Threshold for sufficient decay in fixed-point error to trigger a restart.
necessary_reduction_for_restart	Float64	0.8	Threshold for necessary decay in fixed-point error to trigger a restart.
k_p	Float64	0.99	Proportional gain for the primal weight (PID) controller.
k_i	Float64	0.01	Integral gain for the primal weight (PID) controller.
k_d	Float64	0.0	Derivative gain for the primal weight (PID) controller.
i_smooth	Float64	0.3	Smoothing factor for the integral component of the controller.