SCSSolver in Convex and JuMP

Specific Domains Optimization (Mathematical)
1

The SCS solver is for convex cone problems, but Convex.jl manages to use it to solve quadratic problems; JuMP.jl instead throws an error.

On the other hand, Ipopt seems to be working fine with JuMP but Convex complains.

using Convex, JuMP, SCS, Ipopt

n = 5
s = Convex.Variable(n)
problem = minimize(sumsquares(s))
solve!(problem, SCSSolver()) # this is fine

problem = Model(solver = SCSSolver())
@variable(problem, q[1:n])
@objective(problem, Min, sum(q[i]^2 for i = 1:n))
status = solve(problem) # this throws an error

s = Convex.Variable(n)
problem = minimize(sumsquares(s))
solve!(problem, IpoptSolver()) # this throws an error

problem = Model(solver = IpoptSolver())
@variable(problem, q[1:n])
@objective(problem, Min, sum(q[i]^2 for i = 1:n))
status = solve(problem) # this is fine
2

Maybe the explanation is that Convex.jl knows how to translate sumsquares() into conic form, and therefore feed the problem to SCS.

For JuMP, the problem looks like it requires a LinearQuadratic solver, which SCS isn’t.

For Ipopt, the story is reversed. It does not accept the conic form, but requires expressions, like a Nonlinear solver.

Within MathProgBase, there exist all kinds of bridges between these solver types, but maybe they are missing here.

3

Do you know if this is explained somewhere in Convex Optimization?

4

I think you have better luck with the separate paper on disciplined convex programming by Michael Grant.

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5

Do you mean eq. 13 of book chapter and the discussion in that section?

6

You could also look at the Convex.jl paper. Convex.jl implements disciplined convex programming to turn everything into conic form. JuMP does not.

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