在 R 中执行 SQP 算法

Question

我想运行在 R 中进行以下优化：

$arg\ min \left \{ \sum_{i = 1}^{N} \sum_{j = 1}^{N}\ (\sum_{j=1}^{N} w_{i} * w_{j} * \sigma _{i,j} - \sum_{k=1}^{N} w_{j} * w_{k} * \sigma_{j,k})^2 \right \}$

u.c.: 0 <= x <= 1 和 Sum(x)=1

等式基于：Efficient Algorithms for Computing Risk Parity Portfolio Weights（等式 10）

原作者说用SQP。我想遵循那个，但是如何？

Answer 1

代码可能如下所示：

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

在 R 中执行 SQP 算法

Perform a SQP algorithm in R

r

algorithm

quantitative-finance