R solve.QP 给出“约束不一致，无解！”错误

Question

我已经准备好所有向量和矩阵，并且正确并且仍然可以求解。QP 抛出错误。有人可以帮忙吗？

错误是：

solve.QP(Dmat, dvec, Amat, bvec) 中的错误：
约束不一致，无解！

Dmat=matrix(c(0.002010,  0.002656, -0.001158, -0.001350,  0.000242,  0.000256, -0.000890, -0.000874, 0.002656,  0.014554, -0.002614, -0.001220, -0.004474, -0.001978,  0.002884, -0.003070,-0.001158, -0.002614,  0.119704,  0.055176,  0.126994,  0.046072,  0.065934,  0.096078, -0.001350, -0.001220,  0.055176,  0.059218,  0.053144,  0.042930,  0.041394,  0.059708, 0.000242, -0.004474,  0.126994,  0.053144,  0.204976,  0.085488,  0.079886,  0.131988, 0.000256, -0.001978,  0.046072,  0.042930,  0.085488,  0.064112,  0.039762,  0.064470, -0.000890,  0.002884,  0.065934,  0.041394,  0.079886,  0.039762,  0.056710,  0.070128, -0.000874, -0.003070,  0.096078,  0.059708,  0.131988,  0.064470,  0.070128,  0.159916), nrow=8,ncol=8,byrow=TRUE)

dvec <- rep(0,8)
m = c(.08,.67,6.41,4.08,7.43,3.7,4.8,6.6)/100
tau = .25
omega = diag(x = c(.000801,.009546,.000884))
q = c(.041,.016,.008)
P = rbind(c(0,0,0,0,0,1,0,0),c(0,0,0,0,0,0,-1,1),c(0,0,-1,0,1,0,0,0))
covar = Dmat/2

mhat_1=solve(solve(tau * covar)+(((t(P) %*% solve(omega)) %*% P)))
mhat_2=(solve(tau * covar) %*% m) + ((t(P) %*% solve(omega)) %*% q)
mhat = mhat_1 %*% mhat_2
Amat <- matrix(c(mhat,-mhat,rep(1,8),rep(-1,8),diag(length(mhat))),8,12)

bvec=matrix(c(0.07640375, -0.07640375,  1.00000000, -1.00000000,  0.00000000,  0.00000000, 0.00000000,  0.00000000,  0.00000000,  0.00000000,  0.00000000,  0.00000000),nrow=1,ncol=12,byrow=TRUE)

sol = solve.QP(Dmat,dvec,Amat,bvec)

Answer 1

似乎没有内部解决方案，问题来自在bvec 中使用0.07640375（对应于mhat[5]）。至于允许角落解决方案，只需使用更高的精度并设置

bvec <- matrix(c(0.0764037467, -0.0764037467,  1, -1,  rep(0, 8)), nrow = 1)

相反。那么

solve.QP(Dmat,dvec,Amat,bvec)$sol
# [1]  1.800544e-16  1.577392e-16  5.082845e-09  1.771718e-16  1.000000e+00  1.649150e-16
# [7] -3.161050e-20  0.000000e+00