# Find values that minimize function (by passing list as initial searching points)

I have a cost function and I want to find which variables minimize it using the built-in method FindMinimum

My cost function is this (keep in mind that y is a list)

myCostFunction[y_, target_, expectedProbsTotal_] :=
Module[{n, p, myCost, sumProbs, values, x},

n = 3;
myCost = 0;
sumProbs = 0;

p = Table[0, 3];

For[i = 1, i <= n, i++,

p[[i]] = 1/(1 + Exp[-y[[i]]]);
sumProbs += p[[i]];

]; (* for *)

values = Table[0, 3];

For[i = 1, i <= 3, i++,
values[[i]] = p[[i]]
];

For[i = 1, i <= 3, i++,
x = values[[i]] - target[[i]];
myCost += x*x;
];

myCost = Sqrt[myCost/n] + Abs[sumProbs - expectedProbsTotal];
myCost

]


What I am trying to do, using the syntax found here is to find the values of list y that minimize my cost function, assuming that I have some initial values of

{0.6, -1.12, -1.5}


while myTarget = {1.5, 3.5, 5};

I tried this but it is not working

FindMinimum[
myCostFunction[x, myTarget,
1], {{x[[1]], 0.6}, {x[[2]], -1.12}, {x[[3]], -1.5}}]


the error i get is:

FindMinimum::vloc: The variable x[1] cannot be localized so that it can be assigned to numerical values.

I also tried the constraint x[[1]]+x[[2]]+x[[3]]==1 but it doesn't work either.

FindMinimum[myCostFunction[{x1, x2 , x3}, myTarget,1], {{x1, 0.6}, {x2, -1.12}, {x3, -1.5}}, Method -> "PrincipalAxis"]
(*{3.39899, {x1 -> 0.288232, x2 -> -1.12, x3 -> -1.5}}*)


works.

If list argument x=x1,x2,x3} is an issue:

x = {x1, x2, x3}
FindMinimum[myCostFunction[x, myTarget, 1],MapThread[{#1, #2} &, {x, {0.6,-1.12, -1.5}}], Method -> "PrincipalAxis"]
`

gives the same result.

• I was looking for a syntax like this, excellent, thanks – Fierce82 Jul 25 '18 at 14:11