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chainsing.jl
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chainsing.jl
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using JuMP
using MosekTools
import MathOptInterface
const MOI = MathOptInterface
const MOIU = MathOptInterface.Utilities
"""
Formulate the problem
min. sum_{j=0,...,(n-2)/2} s[j] + t[j] + p[j] + q[j]
s.t. (1/2, s[j], x[i]+10x[i+1]) \in Qr,
(1/2, t[j], 5^{1/2}*(x[i+2]-x[i+3])) \in Qr
(1/2, r[j], (x[i+1]-2x[i+2])) \in Qr
(1/2, u[j], 10^{1/4}*(x[i]-10x[i+3])) \in Qr
(1/2, p[j], r[j]) \in Qr
(1/2, q[j], u[j]) \in Qr, j=0,...,(n-2)/2, i = 2j
0.1 <= x[i] <= 1.1, i=0,2,...,n-2
"""
function chainsing1(M :: Model,n :: Int)
m = (n-2) >> 1
@variable(M,x[1:n])
@variable(M,p[1:m])
@variable(M,q[1:m])
@variable(M,r[1:m])
@variable(M,s[1:m])
@variable(M,t[1:m])
@variable(M,u[1:m])
for j in 1:m
i = ((j - 1) << 1) + 1
# s[j] >= (x[i] + 10*x[i+1])^2
@constraint(M, [ 0.5, s[j], x[i]+10*x[i+1] ] in MOI.RotatedSecondOrderCone(3))
# t[j] >= 5*(x[i+2] - x[i+3])^2
@constraint(M, [ 0.5, t[j], sqrt(5.0)*(x[i+2] - x[i+3]) ] in MOI.RotatedSecondOrderCone(3))
# r[j] >= (x[i+1] - 2*x[i+2])^2
@constraint(M, [ 0.5, r[j], x[i+1] - 2.0*x[i+2] ] in MOI.RotatedSecondOrderCone(3))
# 1/10 * u[j] >= (x[i] - 10*x[i+3])^2
@constraint(M, [ 0.5 * 10^(-1.0), u[j], x[i] - 10.0*x[i+3] ] in MOI.RotatedSecondOrderCone(3))
# p[j] >= r[j]^2
@constraint(M, [ 0.5, p[j], r[j] ] in MOI.RotatedSecondOrderCone(3))
# q[j] >= u[j]^2
@constraint(M, [ 0.5, q[j], u[j] ] in MOI.RotatedSecondOrderCone(3))
end
#0.1 <= x[i] <= 1.1, i=0,2,...,n-2
for i in 1:2:n-1
@constraint(M,x[i] <= 1.1)
@constraint(M,x[i] >= 0.1)
end
@objective(M, Min, sum(s) + sum(t) + sum(p) + sum(q))
end
function chainsing2(M :: Model,n :: Int)
m = (n-2) >> 1
@variable(M,x[1:n])
@variable(M,p[1:m])
@variable(M,q[1:m])
@variable(M,r[1:m])
@variable(M,s)
@variable(M,u[1:m])
se = Array{Any}(2 * m + 2)
#@constraint(M, [ 0.5, s,
# @expression(M, x[i] + 10*x[i+1] for i in 1:2:n-3 )...,
# @expression(M, 5*(x[i+2] - x[i+3]) for i in 1:2:n-3 )... ] in MOI.RotatedSecondOrderCone(2*m+2))
@constraint(M, @expression(M, [ 0.5; s; [ x[i] + 10*x[i+1] for i in 1:2:n-3 ] ; [ 5*(x[i+2] - x[i+3]) for i in 1:2:n-3 ] ] ) in MOI.RotatedSecondOrderCone(2*m+2))
for j in 1:m
i = ((j - 1) << 1) + 1
# r[j] >= (x[i+1] - 2*x[i+2])^2
@constraint(M, [ 0.5, r[j], x[i+1] - 2*x[i+2] ] in MOI.RotatedSecondOrderCone(3))
# u[j] >= sqrt(10)*(x[i] - 10*x[i+3])^2
@constraint(M, [ 0.5 * 10.0^(-1.0), u[j], x[i] - 10*x[i+3] ] in MOI.RotatedSecondOrderCone(3))
# p[j] >= r[j]^2
@constraint(M, [ 0.5, p[j], r[j] ] in MOI.RotatedSecondOrderCone(3))
# q[j] >= u[j]^2
@constraint(M, [ 0.5, q[j], u[j] ] in MOI.RotatedSecondOrderCone(3))
end
#0.1 <= x[i] <= 1.1, i=0,2,...,n-2
for i in 1:2:n-1
@constraint(M,x[i] <= 1.1)
@constraint(M,x[i] >= 0.1)
end
@objective(M, Min, sum(s) + sum(p) + sum(q))
end
function chainsing3(M :: Model,n :: Int)
m = (n-2) >> 1
@variable(M,x[1:n])
@variable(M,p[1:m])
@variable(M,q[1:m])
@variable(M,r[1:m])
@variable(M,s)
@variable(M,u[1:m])
se = Array{Any}(2 * m + 2)
@constraint(M, @expression(M, [ 0.5; s;
[ x[i] + 10*x[i+1] for i in 1:2:n-3 ] ;
[ 5*(x[i+2] - x[i+3]) for i in 1:2:n-3 ] ;
p ; q ]) in MOI.RotatedSecondOrderCone(4*m+2))
for j in 1:m
i = ((j - 1) << 1) + 1
# r[j] >= (x[i+1] - 2*x[i+2])^2
@constraint(M, [ 0.5, r[j], x[i+1] - 2*x[i+2] ] in MOI.RotatedSecondOrderCone(3))
# u[j] >= sqrt(10)*(x[i] - 10*x[i+3])^2
@constraint(M, [ 0.5 * 10.0^(-1.0), u[j], x[i] - 10*x[i+3] ] in MOI.RotatedSecondOrderCone(3))
end
#0.1 <= x[i] <= 1.1, i=0,2,...,n-2
for i in 1:2:n-1
@constraint(M,x[i] <= 1.1)
@constraint(M,x[i] >= 0.1)
end
@objective(M, Min, s)
end
function main(argv :: Vector{String})
n = 8192
backend = :generic
method = 1
timefile = nothing
taskfile = nothing
opt = false
for a in argv
m = match(r"--([^=]+)(?:=(.*))?",a)
if m == nothing
n = parse(Int,argv[1])
else
key = m.captures[1]
val = m.captures[2]
if key == "optimize"
opt = true
elseif key == "method"
method = parse(Int,val)
elseif key == "timefile"
timefile = val
elseif key == "out"
taskfile = val
elseif key == "backend"
if val == "generic" val == nothing
backend = :generic
elseif val == "mock"
backend = :mock
elseif val == "mosek"
backend = :mosek
end
elseif key == "help"
println("Usage: chainsing n [options]")
println(" n The problem scale, the default being 8192. Must be even.")
println("Options:")
println("\t--method=[1|2|3] Which formulation to use")
println("\t--timefile=filename Which formulation to use")
println("\t--backend=[generic|mosek|mock] Which backend to use.")
println("\t\tgeneric Use generic backend, then copy to MOSEK optimizer")
println("\t\tmosek Use mosek as backend")
println("\t\tmock Use generic backend, then copy to JuMP mock optimizer")
println("\t--out=filename Write task to this file")
println("\t--optimize Call optimizer")
return
end
end
end
#println("Chainsing")
#println("\tn : $n")
#println("\tmethod : $method")
#println("\ttimefile : $timefile")
#println("\ttaskfile : $taskfile")
#println("\toptimize : $opt")
#println("\tbackend : $backend")
T = 0.0
m =
if backend == :generic
solver = Mosek.Optimizer()
Model( optimizer = solver)
elseif backend == :mosek
solver = Mosek.Optimizer()
Model( mode = JuMP.Direct, backend = solver)
elseif backend == :mock
solver = MOIU.MockOptimizer(JuMP.JuMPMOIModel{Float64}())
Model( optimizer = solver)
end
if backend == :generic
println("Use: Generic backend, then copy to Mosek")
elseif backend == :mosek
println("Use: Mosek directly as backend")
elseif backend == :mock
println("Use: Generic backend, then copy to mock solver")
end
T0 = time()
if method == 1
chainsing1(m,n)
elseif method == 2
chainsing2(m,n)
elseif method == 3
chainsing3(m,n)
end
if backend != :mosek
MOIU.attachoptimizer!(m)
end
T1 = time()
T = T1-T0
@printf("Model build time: %.2f secs\n",T)
if timefile != nothing
open(timefile, "w") do f
@printf(f,"%.2f", T)
end
end
end
main(ARGS)