Constraints on Positive Moment Sequences
using DynamicPolynomials, MultivariateSeries, MomentTools
using MosekTools; optimizer = Mosek.Optimizer;┌ Info: Precompiling MomentTools [65cd4d85-9fe5-4fdc-93e2-c8798c615752]
└ @ Base loading.jl:1273
┌ Warning: Package MomentTools does not have MultivariateSeries in its dependencies:
│ - If you have MomentTools checked out for development and have
│ added MultivariateSeries as a dependency but haven't updated your primary
│ environment's manifest file, try `Pkg.resolve()`.
│ - Otherwise you may need to report an issue with MomentTools
└ Loading MultivariateSeries into MomentTools from project dependency, future warnings for MomentTools are suppressed.X = @polyvar x y
d = 10
M = MomentModel(X, d, optimizer, nu=2)A Moment program with:
A JuMP Model
Feasibility problem with:
Variables: 462
`Array{JuMP.VariableRef,1}`-in-`MathOptInterface.PositiveSemidefiniteConeTriangle`: 2 constraints
Model mode: AUTOMATIC
CachingOptimizer state: EMPTY_OPTIMIZER
Solver name: Dual model with Mosek attached
Names registered in the model: basis, degree, dual, index, moments, monomials, nu, variables, yconstraint_nneg(M,1, 1-x^2-y^2)
constraint_nneg(M,2, 1-x^2, 1-y^2)L = monomials(X, seq(0:2*d))
lebesgue(i,j) = ((1-(-1)^(i+1))/(i+1))*((1-(-1)^(j+1))/(j+1))
constraint_moments(M,
[(m=>lebesgue(exponents(m)...)) for m in L],
collect(1:2), [1,1] )objective(M, 1, 1.0, "sup")$ y_{1,1} $
v = optimize(M)[1]Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 462
Cones : 0
Scalar variables : 231
Matrix variables : 5
Integer variables : 0
Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 0
Eliminator terminated.
Eliminator started.
Freed constraints in eliminator : 0
Eliminator terminated.
Eliminator - tries : 2 time : 0.00
Lin. dep. - tries : 1 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.00
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 462
Cones : 0
Scalar variables : 231
Matrix variables : 5
Integer variables : 0
Optimizer - threads : 8
Optimizer - solved problem : the primal
Optimizer - Constraints : 462
Optimizer - Cones : 1
Optimizer - Scalar variables : 232 conic : 232
Optimizer - Semi-definite variables: 5 scalarized : 7527
Factor - setup time : 0.01 dense det. time : 0.00
Factor - ML order time : 0.00 GP order time : 0.00
Factor - nonzeros before factor : 5.43e+04 after factor : 8.74e+04
Factor - dense dim. : 2 flops : 5.44e+07
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 3.0e+00 4.0e+00 1.0e+00 0.00e+00 0.000000000e+00 0.000000000e+00 1.0e+00 0.02
1 8.6e-01 1.1e+00 7.4e-02 3.19e-01 2.227313818e+00 2.034785147e+00 2.9e-01 0.03
2 2.0e-01 2.7e-01 8.0e-03 1.62e+00 3.558535953e+00 3.532069682e+00 6.8e-02 0.05
3 5.3e-02 7.1e-02 1.1e-03 1.50e+00 3.775424594e+00 3.770494332e+00 1.8e-02 0.07
4 1.4e-02 1.9e-02 1.6e-04 1.01e+00 3.774265528e+00 3.773107456e+00 4.7e-03 0.09
5 4.9e-03 6.5e-03 4.0e-05 8.08e-01 3.760047982e+00 3.759705942e+00 1.6e-03 0.10
6 2.7e-03 3.6e-03 2.4e-05 3.66e-01 3.749815207e+00 3.749724302e+00 8.9e-04 0.12
7 6.9e-04 9.2e-04 4.9e-06 3.80e-01 3.725437924e+00 3.725569163e+00 2.3e-04 0.14
8 2.4e-04 3.1e-04 1.2e-06 3.25e-01 3.704778259e+00 3.704873452e+00 7.9e-05 0.17
9 1.1e-04 1.4e-04 5.3e-07 2.30e-01 3.691943416e+00 3.692063045e+00 3.6e-05 0.18
10 3.1e-05 4.1e-05 1.0e-07 4.47e-01 3.676385386e+00 3.676448347e+00 1.0e-05 0.20
11 1.1e-05 1.5e-05 3.2e-08 4.65e-01 3.668719992e+00 3.668774291e+00 3.7e-06 0.22
12 6.1e-06 8.2e-06 2.0e-08 2.94e-02 3.664551877e+00 3.664634224e+00 2.0e-06 0.24
13 3.2e-06 4.3e-06 1.2e-08 -1.56e-01 3.657723571e+00 3.657826546e+00 1.1e-06 0.26
14 1.1e-06 1.5e-06 3.4e-09 1.35e-01 3.645081107e+00 3.645162092e+00 3.6e-07 0.28
15 3.8e-07 4.9e-07 1.1e-09 1.24e-01 3.633102930e+00 3.633176735e+00 1.2e-07 0.29
16 2.3e-07 2.8e-07 6.8e-10 -1.62e-03 3.627183700e+00 3.627277402e+00 6.9e-08 0.31
17 9.2e-08 1.2e-07 2.8e-10 4.23e-02 3.615519444e+00 3.615608628e+00 2.9e-08 0.33
18 1.6e-08 2.9e-08 5.5e-11 1.94e-01 3.599258722e+00 3.599314907e+00 7.2e-09 0.35
19 5.8e-09 1.0e-08 1.5e-11 5.22e-01 3.591755197e+00 3.591786889e+00 2.6e-09 0.38
20 1.7e-09 3.0e-09 2.5e-12 7.78e-01 3.587479170e+00 3.587490742e+00 7.4e-10 0.41
21 7.7e-10 1.4e-09 9.0e-13 7.69e-01 3.586171166e+00 3.586178254e+00 3.4e-10 0.44
22 6.1e-10 8.9e-10 5.9e-13 5.74e-01 3.585752489e+00 3.585759466e+00 2.2e-10 0.47
23 3.7e-10 5.4e-10 3.2e-13 4.66e-01 3.585225807e+00 3.585231576e+00 1.3e-10 0.50
24 1.9e-10 2.7e-10 1.6e-13 2.65e-01 3.584589117e+00 3.584594599e+00 6.7e-11 0.53
25 1.9e-10 2.7e-10 1.6e-13 4.02e-01 3.584580797e+00 3.584586260e+00 6.7e-11 0.56
26 1.8e-10 2.5e-10 1.4e-13 3.99e-01 3.584512733e+00 3.584518052e+00 6.2e-11 0.60
27 8.7e-11 1.1e-10 5.5e-14 3.85e-01 3.583843540e+00 3.583847594e+00 2.7e-11 0.63
28 8.1e-11 8.4e-11 3.8e-14 3.28e-01 3.583633435e+00 3.583636690e+00 2.1e-11 0.65
29 7.9e-11 8.2e-11 3.7e-14 5.30e-01 3.583619139e+00 3.583622347e+00 2.1e-11 0.69
30 7.8e-11 8.2e-11 3.7e-14 6.05e-01 3.583618683e+00 3.583621889e+00 2.1e-11 0.73
31 7.8e-11 8.2e-11 3.7e-14 5.50e-01 3.583618683e+00 3.583621889e+00 2.1e-11 0.77
32 7.8e-11 8.2e-11 3.7e-14 5.60e-01 3.583618683e+00 3.583621889e+00 2.1e-11 0.82
Optimizer terminated. Time: 0.90
3.5836218894780534