Question

我正在尝试使用auglag或Rsolnp找到以下优化问题的解决方案。

Max t(w1 - w2) * Kf * Sf * t(Kf) * (w1 - w2)
subject to Kc * w1 = Kc * w2
and sum(w1) = 1 and sum(w2) = 1 and w1,w2 >= 0
Sc and Sf are variance covariance matrices at the coarse and fine level respectively.
Kc and Kf are exposure matrices as the coarse and fine level respectively.
Nc and Nf are nodes at which exposure nodes at the coarse and fine level.

这有效地试图找到两个投资组合w1和w2的wts，其将在更精细的曝光水平下最大化TEV，受到wts = 1和所有wts＆gt;的总和的影响。 0.还有另一个平等约束（这实际上意味着两个投资组合的粗略水平相同）。 Rsolnp无法最大化并返回一个解决方案，其中目标函数为0并且auglag完全爆炸并且不满足一系列警告的约束。

任何人都可以帮助我了解我哪里出错了吗？

    seqFineNodes <- c(1, 2, 3, 4, 5, 6)

Nc <- c(2, 3, 5)

Kc <- matrix(c(0.2481316799436,0.495478766935844,0,0,0,0,0,0,0.743360061619584,0.497321712603124,0,0,0,0,0,0.497321712603124,1.23913608908603,1.48240730986596), nrow=length(seqFineNodes), ncol=length(Nc))
dimnames(Kc) <- list(as.character(seqFineNodes), as.character(Nc))

Sc <- matrix(c(619.806079280659,627.832850585004,549.805085990891,627.832850585004,668.726833059322,624.524848194842,549.805085990891,624.524848194842,696.498483673357), nrow=length(Nc), ncol=length(Nc))
dimnames(Sc) <- list(as.character(Nc), as.character(Nc))

Nf <- c(2, 3, 4, 5)

Kf <- matrix(c(0.2481316799436,0.495478766935844,0,0,0,0,0,0,0.743360061619584,0,0,0,0,0,0,0.994643425206249,0,0,0,0,0,0,1.23913608908603,1.48240730986596), nrow=length(seqFineNodes), ncol=length(Nf))
dimnames(Kf) <- list(as.character(seqFineNodes), as.character(Nf))

Sf <- matrix(c(619.806079280659,627.832850585004,602.504944834256,549.805085990891,627.832850585004,668.726833059322,666.196728425214,624.524848194842,602.504944834256,666.196728425214,696.688027074344,681.064062606848,549.805085990891,624.524848194842,681.064062606848,696.498483673357), nrow=length(Nf), ncol=length(Nf))
dimnames(Sf) <- list(as.character(Nf), as.character(Nf))

KRD_fine <- Kf
KRD_coarse <- Kc
VC_fine <- Sf
VC_coarse <- Sc
countw <- length(seqFineNodes)


t1 <- diag(x = 1, nrow = countw, ncol = countw)
t2 <- diag(x = -1, nrow = countw, ncol = countw)
tr <- cbind(t1,t2)

D_fine <- t(tr) %*% KRD_fine %*% VC_fine %*% t(KRD_fine) %*% tr
#round(eigen(Dmat)$values, 4)
D_fine <- as.matrix(nearPD(D_fine)$mat)
#round(eigen(Dmat)$values, 4)

eq_coarse_krd_A <- t(KRD_coarse) %*% tr
eq_coarse_krd_b <- rep(0, nrow(VC_coarse))

# Equality constraints
eq_A1 <- c(rep(1, countw), rep(0,countw))
eq_A2 <- c(rep(0, countw), rep(1,countw))
eq_b <- c(1 , 1)

# Constraint wts greater than zero
ineq_A <- diag(x = 1, nrow = 2 * countw, ncol = 2 * countw)
ineq_b <- rep(0, 2 * countw)

# Combine constraints
heq <- rbind(eq_coarse_krd_A, eq_A1, eq_A2)
beq <- c(eq_coarse_krd_b, eq_b)

hin <- ineq_A

theta <- c(1, rep(0, countw - 1), 1, rep(0, countw - 1))

krdsol <- solnp(par = theta, 
                fun = function(x) -c(t(x) %*% D_fine %*% x), 
                ineqfun = function(x) c(hin %*% x),
                ineqLB = rep(0, 2 * countw),
                ineqUB = rep(1, 2 * countw),
                eqfun = function(x) c(heq %*% x),
                eqB = beq)


krdFine <- auglag(par = theta, 
                  fn = function(x) c(t(x) %*% D_fine %*% x), 
                  hin = function(x) c(hin %*% x),
                  heq = function(x) c(heq %*% x) - beq,
                  control.outer = list(method = "nlminb"),
                  control.optim=list(fnscale=-1))

Answer 1

我解决了您关于solnp的问题。 ?solnp说fun，ineqfun和eqfun返回vector但你的回复matrix。所以我向他们添加了c(...)。

library(Rsolnp)

krdsol <- solnp(par = theta, 
                fun = function(x) c(-t(x) %*% D_fine %*% x), 
                ineqfun = function(x) c(hin %*% x),
                ineqLB = rep(0, 2 * countw),
                ineqUB = rep(1, 2 * countw),
                eqfun = function(x) c(heq %*% x),
                eqB = beq)

将帖子

作为参数的元素auglag(control.optim=list(...))列在?nlminb()中（并参见?auglag()）

在R：Rsolnp或Auglag中使用线性约束最大化二次目标

1 个答案: