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.