I got “unknown status” when I run the following code
using MultivariatePolynomials
using JuMP
using PolyJuMP
using SumOfSquares
using DynamicPolynomials
using Mosek
using SemialgebraicSets
@polyvar x
m = SOSModel(solver = MosekSolver(MSK_IPAR_INTPNT_MAX_ITERATIONS=1000, MSK_DPAR_ANA_SOL_INFEAS_TOL=1e-14))
@variable m a
@variable m b
@variable m c
epsilon = 2.520204237306060e-5
x_min = -3*pi/2
x_max = -pi/2
p = -1 + (x+pi)^2/factorial(2) - (x+pi)^4/factorial(4) + (x+pi)^6/factorial(6) - (x+pi)^8/factorial(8) + (x+pi)^10/factorial(10) -(x+pi)^12/factorial(12) +(x+pi)^14/factorial(14) - epsilon - a*x^2 - b*x - c
s = @set x >= x_min && x <= x_max
@objective m Min (sin(x_max) - 1/3*a*x_max^3 - 1/2*b*x_max^2 - c*x_max - sin(x_min) + 1/3*a*x_min^3 + 1/2*b*x_min^2 + c*x_min )
@constraint( m, p >= 0, domain = s)
solve(m)
println("a =", getvalue(a))
println("b =", getvalue(b))
println("c =", getvalue(c))
However, Mosek could solve the problem optimally when I reduced the polynomial degree in the Taylor series to “6”. Can you please let me know what should I do to avoid this kind of problems. Thanks in advance!