python - 使用R:Rsolnp或Auglag中的线性约束最大化二次目标

我试图用auglag或Rsolnp来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.

这是有效地试图找到WTs的两个投资组合W1和W2，将最大化TEV在更精细的暴露水平，受WTS＝1和所有WTS＞0的总和。还有另一个等式约束（这实际上意味着两个投资组合的粗略风险敞口是相同的）。RSOLNP未能最大化，并给出了一个解决方案，其中目标函数是0，并且AuffRAG完全被吹起，并且不满足约束，也有一堆警告。
有谁能帮我弄明白我错在哪里吗？

    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))

最佳答案

我解决了你关于solnp的问题。?solnp表示fun，ineqfun和eqfun返回vector但您的返回matrix。所以我把c(...)添加到它们中。

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)

[编辑]
auglag(control.optim=list(...))接受的元素作为参数列在?nlminb()中（请参见?auglag()）

关于python - 使用R:Rsolnp或Auglag中的线性约束最大化二次目标，我们在Stack Overflow上找到一个类似的问题：https://stackoverflow.com/questions/39401978/