This code implements the example in the Clarabel "Getting Started" documentation

using Clarabel, SparseArrays, LinearAlgebra

P = sparse([3. 1 -1; 0 4 2; 0 0 5])

q = [1,2,-3.]

3-element Vector{Float64}:
  1.0
  2.0
 -3.0

equality constraint

Aeq = [1. 1. -1.]
beq = [1.]

1-element Vector{Float64}:
 1.0

inequality constraint

Aineq = [0. 1. 0.;
         0. 0. 1.]
bineq = [2.,2.]

2-element Vector{Float64}:
 2.0
 2.0

SOC constraint

Asoc = -I(3)*1.
bsoc = [0.,0.,0.]

3-element Vector{Float64}:
 0.0
 0.0
 0.0

Clarabel.jl constraint data

A = sparse([Aeq; Aineq; Asoc])
b = [beq;bineq;bsoc]

cones = [Clarabel.ZeroConeT(1),
         Clarabel.NonnegativeConeT(2),
         Clarabel.SecondOrderConeT(3)]

settings = Clarabel.Settings(verbose = true, time_limit = 5)

solver   = Clarabel.Solver()

Clarabel.setup!(solver, P, q, A, b, cones, settings)

solution = Clarabel.solve!(solver)

>>> Clarabel - Results
Status: SOLVED
Iterations: 6
Objective: 2.397
Solve time: 1.12ms

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