Increase performance of SOC constraints about jump.jl HOT 4 CLOSED

using JuMP
using BenchmarkTools
import Gurobi

const GRB_ENV = Gurobi.Env()
grb_optimizer() = Gurobi.Optimizer(GRB_ENV)

function add_linear(N)
    model = Model(grb_optimizer)
    @variable(model, x)
    @variable(model, y)
    @variable(model, z)
    for _ in 1:N
        @constraint(model, x + y + z <= 1)
    end
    return model
end

function add_soc(N)
    model = Model(grb_optimizer)
    @variable(model, x)
    @variable(model, y)
    @variable(model, z)
    vec = [1, y, z]
    for _ in 1:N
        @constraint(model, [x; vec] in SecondOrderCone())
    end
    return model
end

function add_soc_variables(N)
    model = Model(grb_optimizer)
    @variable(model, x)
    @variable(model, y)
    @variable(model, z)
    for _ in 1:N
        @constraint(model, [x, y, z] in SecondOrderCone())
    end
    return model
end

@benchmark add_linear(100)
@benchmark add_soc(100)
@benchmark add_soc_variables(100)

julia> @benchmark add_linear(100)
BenchmarkTools.Trial: 5224 samples with 1 evaluation.
 Range (min … max):  855.013 μs …   6.484 ms  ┊ GC (min … max): 0.00% … 50.29%
 Time  (median):     920.186 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   953.208 μs ± 260.691 μs  ┊ GC (mean ± σ):  1.10% ±  3.54%

       ▂▄▇██▇▆▅▄▄▃▁▂▂▂▂▁▁▁▁▁                                    ▂
  ▄▄▁▅███████████████████████████▇█▆▆▆▇▆▇▃▅▅▆▅▄▆▅▆▄▃▅▆▃▆▅▁▅▅▃▅▄ █
  855 μs        Histogram: log(frequency) by time       1.26 ms <

 Memory estimate: 157.70 KiB, allocs estimate: 3528.

julia> @benchmark add_soc(100)
BenchmarkTools.Trial: 1146 samples with 1 evaluation.
 Range (min … max):  3.405 ms …   9.597 ms  ┊ GC (min … max): 0.00% … 48.91%
 Time  (median):     4.417 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   4.355 ms ± 468.127 μs  ┊ GC (mean ± σ):  0.52% ±  3.38%

    ▁▁ ▁▂▂                          ▂▂▂ ▁▆██▇▅▄▄▄▄▃▂ ▁        ▁
  ▄▇████████▇██▆█▇▇▆▇▄█▅▆▄▁▆▆▁▆▄▆▅▅██████████████████████▁▁▁▅ █
  3.4 ms       Histogram: log(frequency) by time      4.86 ms <

 Memory estimate: 242.95 KiB, allocs estimate: 4631.

julia> @benchmark add_soc_variables(100)
BenchmarkTools.Trial: 3678 samples with 1 evaluation.
 Range (min … max):  1.211 ms …   7.100 ms  ┊ GC (min … max): 0.00% … 51.24%
 Time  (median):     1.324 ms               ┊ GC (median):    0.00%
 Time  (mean ± σ):   1.355 ms ± 245.645 μs  ┊ GC (mean ± σ):  0.60% ±  2.75%

          ▁█▇▅▃                                                
  ▂▁▁▁▂▃▄▅██████████▇▇▇▆▆▅▄▄▄▄▃▃▃▃▃▃▃▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂ ▃
  1.21 ms         Histogram: frequency by time        1.69 ms <

 Memory estimate: 111.09 KiB, allocs estimate: 2928.

import ProfileView
@profview add_soc(100)

julia> GC.gc(); @time add_linear(100_000);
  0.077155 seconds (1.40 M allocations: 101.363 MiB, 17.74% gc time)

julia> GC.gc(); @time add_soc(100_000);
  0.128777 seconds (1.80 M allocations: 143.006 MiB, 26.64% gc time)

julia> GC.gc(); @time add_soc_variables(100_000);
  0.032610 seconds (802.13 k allocations: 55.587 MiB)

julia> GC.gc(); @time add_linear(100_000);
  0.073181 seconds (1.40 M allocations: 101.363 MiB, 15.95% gc time)

julia> GC.gc(); @time add_soc(100_000);
  0.125340 seconds (1.80 M allocations: 143.006 MiB, 26.69% gc time)

julia> GC.gc(); @time add_soc_variables(100_000);
  0.040289 seconds (802.13 k allocations: 55.587 MiB)