SIP is reported solved but there is constraint violation.

SIP_example3.jl

using EAGO, Plots,Ipopt, JuMP
const Maxi = 1.4

function gsip_1(x,w)

	denom = ((w[1]^2 + 1) * (10^-6  *w[1]^2 + 1)) 

	gsip= 1/(
		w[1]* sqrt(w[1]^2+1)*
		sqrt( 
		((x[3]*w[1]-x[2]/w[1])*(
		- (1.001 *w[1] * sin(w[1]))/(denom) 
		- (0.001*w[1]^2*cos(w[1]))/(denom) 
		+ (cos(w[1]))/(denom) )
		+ 
		x[1]*(
			(0.001*w[1]^2*sin(w[1]))/denom
			- sin(w[1])/denom
			-(1.001)*w[1]*cos(w[1])/denom
		)
		)^2 
		+
		(
			-(x[3]*w[1]-x[2]/w[1])*(
				(0.001 *w[1]^2 * sin(w[1]))/(denom) 
				- sin(w[1])/denom
				-(1.001)*w[1]*cos(w[1])/denom
			)
			+ x[1]*(
				-(0.001*w[1]^2*cos(w[1]))/denom
				+ cos(w[1])/denom
				-(1.001)*w[1]*sin(w[1])/denom
			)
		+1 )^2
		))

		return gsip - x[4]
end
function gsip_2(x,w)
	denom = ((w[1]^2 + 1) * (10^-6  *w[1]^2 + 1)) 

	gsip= 1/(
		sqrt( 
		((x[3]*w[1]-x[2]/w[1])*(
		- (1.001 *w[1] * sin(w[1]))/(denom) 
		- (0.001*w[1]^2*cos(w[1]))/(denom) 
		+ (cos(w[1]))/(denom) )
		+ 
		x[1]*(
			(0.001*w[1]^2*sin(w[1]))/denom
			- sin(w[1])/denom
			-(1.001)*w[1]*cos(w[1])/denom
		)
		)^2 
		+
		(
			-(x[3]*w[1]-x[2]/w[1])*(
				(0.001 *w[1]^2 * sin(w[1]))/(denom) 
				- sin(w[1])/denom
				-(1.001)*w[1]*cos(w[1])/denom
			)
			+ x[1]*(
				-(0.001*w[1]^2*cos(w[1]))/denom
				+ cos(w[1])/denom
				-(1.001)*w[1]*sin(w[1])/denom
			)
		+1 )^2
		))	
		return gsip - Maxi
end


f(x) = x[4]
p_l = Float64[0.01]
p_u = Float64[20.0]
x_l = Float64[0.01, 1e-2, 1e-2, 0.01]
x_u = Float64[1.0, 1.0, 1., 10.]

sip_result = sip_solve(SIPHybrid(), x_l, x_u, p_l, p_u, f, Any[gsip_1,gsip_2], abs_tolerance = 1E-5)
# Algorithm Converged
# SIPResult(1, 1, 1.0878223933552882, 1.0878152321594068, true, [1.0, 0.9777539375595354, 0.27747732688369253, 1.0878223933552882], [0.0], 18.401670217514038)

# can see that there is a violatoin.
x=sip_result.xsol

w_list = exp10.(collect(log10(p_l[1]):0.01:log10(p_u[1])));
gsip1=ones(length(w_list));
gsip2=ones(length(w_list));
for i =1:length(w_list)
	gsip2[i] = gsip_2(x,[w_list[i]])
	gsip1[i]= gsip_1(x,[w_list[i]])
end
p1=plot(log10.(w_list),(gsip2))
plot!(log10.(w_list),(ones(length(Ms))*0.0),colour="red",width = 2)
p2=plot(log10.(w_list),gsip1)
plot(p1,p2,layout=(2,1))