R minimize portfolio function with gradient

Question

I want to minimize function

f <- function(u){ return(-(1+u[1]+u[2]+u[3]+u[4])) }

with gradient grad

And I have constraints:

1) u[1]+u[2]+u[3]+u[4] = 1

2) 0<=u[1]<=1, 0<=u[2]<=1, 0<=u[3]<=1, 0<=u[4]<=1

How to make it correctly? I can make it only for 2 constraint

optim(par=c(0,0,0,0), fn=f,lower=c(0, 0, 0, 0), upper=c(1, 1, 1, 1),method="L-BFGS-B")

But 1 constraint is not true in this case

Thank you, but its incorrect too because if i make lower=c(0.5, 0.5, 0.5, 0.5) result will be 0.5 0.5 0.5 0.5 (1 constraint will be wrong) — Ильшат Мурзурбеков
– Ильшат Мурзурбеков, Commented Feb 1, 2020 at 18:30
Since the sum of the u's equals 1because of (1) the objective function, f, equals -2 regardless of the u values. — G. Grothendieck
– G. Grothendieck, Commented Feb 1, 2020 at 19:48
@G.Grothendieck sure, i know it. it was comment to idea to make f = (u1+u2+u3+u4-1) and minimize it. In my task in zero iteration capital = 1 and u's is profitability.(This comment was deleted) — Ильшат Мурзурбеков
– Ильшат Мурзурбеков, Commented Feb 2, 2020 at 6:02

ThomasIsCoding · Accepted Answer · 2020-02-02 07:59:27Z

1

Maybe you can try fmincon from package pracma like below

pracma::fmincon(c(0,0,0,0), f, gr = grad, Aeq = cbind(1,1,1,1), beq = 1, lb = c(0,0,0,0), ub = c(1,1,1,1))

answered Feb 1, 2020 at 19:15

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3 Comments

It seems like true solution but i have Argument 'Aeq' must be a matrix with length(x0) columns. Though length(x0) = length(Aeq) = 4

Got it. Aeq = cbind(1,1,1,1)

@ИльшатМурзурбеков Great that you fixed it. Does this address your question?