DSDP.jl

DSDP.jl is a wrapper for the DSDP solver.

Warning

DSDP uses the dual-scaling algorithm which makes it highly sensitive to the Slater condition. If your problem does not satisfy this condition, it may report incorrect answers as OPTIMAL. See Use with JuMP section for more details.

It has two components:

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

Affiliation

This wrapper is maintained by the JuMP community and is not an official project of the DSDP developers.

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.

Installation

Install DSDP as follows:

import Pkg
Pkg.add("DSDP")

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

To use a custom binary, read the Custom solver binaries section of the JuMP documentation.

Use with JuMP

To use DSDP with JuMP, use DSDP.Optimizer. It is recommended to remove the Variable.FreeBridge as will prevent the dual to have an interior solution which will break the Slater condition on which the dual-scaling algorithm used by DSDP heavily relies.

using JuMP, DSDP
model = Model(DSDP.Optimizer)
remove_bridge(model, MOI.Bridges.Variable.FreeBridge)

This will also remove support for free variable for your model. If your problem has free variables, it is recommended to dualize it. The dual operation of the Variable.FreeBridge is the Constraint.SplitIntervalBridge so you will have to remove it for the same reason:

using JuMP, Dualization, DSDP
model = Model(dual_optimizer(DSDP.Optimizer))
remove_bridge(model, MOI.Bridges.Constraint.SplitIntervalBridge)

This will also remove support for equality constraints for your model. If your model has equality constraints, prefer not adding a dual_optimizer layer. If your model has both free variables and equality constraints, you're out of luck, another solver not based on the dual-scaling algorithm may be more appropriate is there is no way to reformulate the model.

MathOptInterface API

The DSDP optimizer supports the following constraints and attributes.

List of supported objective functions:

• MOI.ObjectiveFunction{MOI.ScalarAffineFunction{Float64}}

List of supported variable types:

• MOI.Nonnegatives
• MOI.PositiveSemidefiniteConeTriangle

List of supported constraint types:

• MOI.ScalarAffineFunction{Float64} in MOI.EqualTo{Float64}

List of supported model attributes:

• MOI.ObjectiveSense()

Compile your own binaries

In order to compile your own libdsdp.so to be used of DSDP.jl, use the following

OB_DIR=$(julia --project=. -e 'import OpenBLAS32_jll; println(OpenBLAS32_jll.OpenBLAS32_jll.artifact_dir)')
OB="-L${LIBOB_DIR}/lib -lopenblas"
make DSDPCFLAGS="-g -Wall -fPIC -DPIC" LAPACKBLAS="$OB" dsdplibrary
make DSDPCFLAGS="-g -Wall -fPIC -DPIC" LAPACKBLAS="$OB" SH_LD="${CC} ${CFLAGS} -Wall -fPIC -DPIC -shared $OB" oshared