中的R

Question

執行SQP算法

我想R中運行下列優化：

UC：0 < = X < = 1，以及Sum（X）= 1

方程式基於：Efficient Algorithms for Computing Risk Parity Portfolio Weights（公式10）

原始作者說使用SQP。我想遵循但如何？

Answer 1

的代碼看起來是這樣的：

fn <- function(w){return( 
     ((w[1] * w %*% Mat[1,]) - (w[1] * w %*% Mat[1,]))^2 + 
     ((w[1] * w %*% Mat[1,]) - (w[2] * w %*% Mat[2,]))^2 + 
     ((w[1] * w %*% Mat[1,]) - (w[3] * w %*% Mat[3,]))^2 + 

     ((w[2] * w %*% Mat[2,]) - (w[1] * w %*% Mat[1,]))^2 + 
     ((w[2] * w %*% Mat[2,]) - (w[2] * w %*% Mat[2,]))^2 + 
     ((w[2] * w %*% Mat[2,]) - (w[3] * w %*% Mat[3,]))^2 + 

     ((w[3] * w %*% Mat[3,]) - (w[1] * w %*% Mat[1,]))^2 + 
     ((w[3] * w %*% Mat[3,]) - (w[2] * w %*% Mat[2,]))^2 + 
     ((w[3] * w %*% Mat[3,]) - (w[3] * w %*% Mat[3,]))^2 
) 
    } 

    library(Rsolnp) 

    #start values 
    w0 <- c(0.3, 0.6, 0.1) 

    #constrain function 
    eqcon <- function(w){(w[1]+w[2]+w[3])} 
    ebcon <- 1 

    #optimizer 
    sqp <- solnp(pars = w0, 
       fun = fn2, 
       eqfun = eqcon, 
       eqB = ebcon, 
       LB = c(0,0,0), 
       UB = c(1,1,1)) 

    sqp$pars