README.md

SCS

Julia wrapper for the SCS splitting cone solver. SCS can solve linear programs, second-order cone programs, semidefinite programs, exponential cone programs, and power cone programs.

Installation

Install SCS.jl using the Julia package manager:

import Pkg; Pkg.add("SCS")

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

Usage

Use with Convex.jl

This example shows how we can model a simple knapsack problem with Convex and use SCS to solve it.

using Convex, SCS
items  = [:Gold, :Silver, :Bronze]
values = [5.0, 3.0, 1.0]
weights = [2.0, 1.5, 0.3]

# Define a variable of size 3, each index representing an item
x = Variable(3)
p = maximize(x' * values, 0 <= x, x <= 1, x' * weights <= 3)
solve!(p, SCS.Optimizer)
println([items x.value])
# [:Gold 0.9999971880377178
#  :Silver 0.46667637765641057
#  :Bronze 0.9999998036351865]

Use with JuMP

This example shows how we can model a simple knapsack problem with JuMP and use SCS to solve it.

using JuMP, SCS
items  = [:Gold, :Silver, :Bronze]
values = Dict(:Gold => 5.0,  :Silver => 3.0,  :Bronze => 1.0)
weight = Dict(:Gold => 2.0,  :Silver => 1.5,  :Bronze => 0.3)

model = Model(SCS.Optimizer)
@variable(model, 0 <= take[items] <= 1)  # Define a variable for each item
@objective(model, Max, sum(values[item] * take[item] for item in items))
@constraint(model, sum(weight[item] * take[item] for item in items) <= 3)
optimize!(model)
println(value.(take))
# 1-dimensional DenseAxisArray{Float64,1,...} with index sets:
#     Dimension 1, Symbol[:Gold, :Silver, :Bronze]
# And data, a 3-element Array{Float64,1}:
#  1.0000002002226671
#  0.4666659513182934
#  1.0000007732744878

Options

All SCS solver options can be set through Convex.jl or MathOptInterface.jl.

For example:

model = Model(optimizer_with_attributes(SCS.Optimizer, "max_iters" => 10))

# via MathOptInterface:
optimizer = SCS.Optimizer()
MOI.set(optimizer, MOI.RawParameter("max_iters"), 10)
MOI.set(optimizer, MOI.RawParameter("verbose"), 0)

Common options are:

• max_iters: the maximum number of iterations to take
• verbose: turn printing on (1) or off (0) See the glbopts.h header for other options.

Select one of the linear solvers using the linear_solver option. The values available are SCS.DirectSolver (the default) and SCS.IndirectSolver. A third option for using a GPU is experimental, see the section below.

SCS on GPU

An experimental SCS.GpuIndirectSolver can be used on Linux. Note that CUDA_jll must be installed and loaded *before SCS.

julia> import Pkg

julia> Pkg.add(Pkg.PackageSpec(name = "CUDA_jll", version = "10.1"))

julia> using CUDA_jll  # This must be called before `using SCS`.

julia> using SCS

julia> SCS.available_solvers
3-element Array{DataType,1}:
 SCS.DirectSolver
 SCS.IndirectSolver
 SCS.GpuIndirectSolver

julia> optimizer = SCS.Optimizer();

julia> MOI.set(
           optimizer,
           MOI.RawParameter("linear_solver"),
           SCS.GpuIndirectSolver,
       )

Low-level wrapper

SCS.jl provides a low-level interface to solve a problem directly, without interfacing through MathOptInterface.

This is an advanced interface with a risk of incorrect usage. For new users, we recommend that you use the JuMP or Convex interfaces instead.

SCS solves a problem of the form:

minimize        1/2 * x' * P * x + c' * x
subject to      A * x + s = b
                s in K

where K is a product cone of:

• zero cone
• positive orthant { x | x ≥ 0 }
• box cone { (t,x) | t*l ≤ x ≤ t*u}
• second-order cone (SOC) { (t,x) | ||x||_2 ≤ t }
• semi-definite cone (SDC) { X | X is psd }
• exponential cone { (x,y,z) | y e^(x/y) ≤ z, y>0 }
• power cone { (x,y,z) | x^a * y^(1-a) ≥ |z|, x ≥ 0, y ≥ 0 }
• dual power cone { (u,v,w) | (u/a)^a * (v/(1-a))^(1-a) ≥ |w|, u ≥ 0, v ≥ 0 }.

To solve this problem with SCS, call SCS.scs_solve; see the docstring for details.