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 Post subject: Alglib minnlc returns solution out of constraintsPosted: Wed May 06, 2020 1:23 pm

Joined: Wed May 06, 2020 1:10 pm
Posts: 1
I am trying to implement a simple minimisation under a quadratic inequality constraint and a linear equality constraint as well as lower and upper bounds. My problem is as follow:

min: x1*(-0.00498) + x2*0.05656

u.c. :

. x1^2 * 0.00001048 + 2*x1*x2*0.001431 + x2^2*0.6737996 <= 0.0084050
. x1 + x2 = 1.0
. 0 < x1 < 0.9
. 0 < x2 < 0.9

Once implemented in F# using Alglib it seems that the constraints are not respected. Neither the sum x1+x2 is equal to 1.0 nor the variance is below 0.0084. Though lower and upper bound are respected, my objective function with x2 is improved (lower) than with x0. I believe I have an issue with my formulation of the constraints, but I can't see which one.

let nsfunc2_jac(x:float[]) (fi:float[])(jac:float[,])=
fi.[0] <- -(x.[0]*-0.00498+x.[1]*0.05656)
fi.[2] <- x.[0]+x.[1]+x.[2]-1.0
fi.[1] <- x.[0]*x.[0]*0.00001048 + 2.0*x.[0]+x.[1]*0.001431 + x.[1]*x.[1]*0.6737996-0.0084050
jac.[0,0] <- -0.00498
jac.[0,1] <- 0.05656
jac.[2,0] <- 1.0
jac.[2,1] <- 1.0
jac.[1,0] <- 2*x.[0]*0.00001048 + 2*x[1]*0.001431
jac.[1,1] <- 2*x.[0]*0.001431 + 2+x[1]*0.6737996

let mutable state2 = new alglib.minnlcstate()
let mutable rep2 = new alglib.minnlcreport()
let mutable nrep = new alglib.ndimesional_rep(func2)
let x0 = [|0.8999, 0.1001|]
alglib.minnlccreate(2,x0, &state2)
alglib.minnlcsetalgoaul(state2, 1000.0, 15.0)
alglib.minnlsetcond(state2, 0.000001,10.0)
alglib.minnlcsetscale(state2, [|1.0,1.0|])
alglib.minnlcsetprecexactlowrank(state2, 5.0)
alglib.minnlcsetnlc(state2, 1,1)
alglib.minnlcsetbc(state2, [|0.0,0.0|], [|0.9,0.9|])

alglib.minnlcoptimize(state2, jac, nrep, None)
let x2, rep = alglib.minnlcresults(state2)
let var = x2.[0]*x2.[0]*0.00001048 + 2.0*x2.[0]+x2.[1]*0.001431 + x2.[1]*x2.[1]*0.6737996
printfn "Variance: %s" var.ToString()
I get Var = 0.53 well above the 0.0084050 target. In fact, after the first iteration both my equality and my inequality constraints are broken and the algorithm never comes back within the range.

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