SIP test problem 2

SIP_example2.jl

# Test problem 5 in Watson (1983).  
# Mitsos reports solving this problem with the result
#  x =[1.009, -0.1472,-0.3601]
# f(x) = 4.320798635665406
# Using SIPHybrid gives # 4.320798635665406

# again issue with exp?
f(x) = exp(x[1])+exp(x[2])+exp(x[3])
gSIP(x,p) = 1/(1+p[1]^2) - x[1] - x[2]*p[1]-x[3]*p[1]^2
x_l = Float64[-1000.0, -1000.0,-1000.0]
x_u = Float64[1000.0, 1000.0,1000.0]
p_l = Float64[0.0]
p_u = Float64[1.0]


sip_result = sip_solve(SIPHybrid(), x_l, x_u, p_l, p_u, f, Any[gSIP], abs_tolerance = 1E-8,)
# SIPResult(1, 1, 4.320798635665406, 4.320798635665406, true, [1.0000918203231945, -0.011069365269669004, -0.48894097011504023], [0.0], 3.5921216011047363)

# using nicer bounds
x_l = Float64[-100.0, -100.0,-100.0]
x_u = Float64[100.0, 100.0,100.0]
sip_result = sip_solve(SIPHybrid(), x_l, x_u, p_l, p_u, f, Any[gSIP], abs_tolerance = 1E-8,)
# SIPResult(1, 1, 4.301416382263877, 4.301416382263877, true, [1.0071612929616767, -0.13185663329599862, -0.37522940388048637], [0.0], 0.9766333103179932)