ordinalRegressionLoss: The loss function for ordinal regression
In bmrm: Bundle Methods for Regularized Risk Minimization Package
Description
Usage
Arguments
Value
References
See Also
Examples
Description
The loss function for ordinal regression
Usage
1
ordinalRegressionLoss(x, y, C = "0/1", impl = c("loglin", "quadratic"))
Arguments
x
matrix of training instances (one instance by row)
y
integer vector of positive values (>=1) representing the training labels for each instance in x
C
the cost matrix to use, C[i,j] being the cost for predicting label i instead of label j.
impl
either the string "loglin" or "quadratic", that define the implementation to use for the computation of the loss.
Value
a function taking one argument w and computing the loss value and the gradient at point w
References
Teo et al.
Bundle Methods for Regularized Risk Minimization
JMLR 2010
See Also
nrbm
Examples
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
# -- Load the data
x <- data.matrix(iris[1:4])
y <- as.integer(iris$Species)
# -- Train the model
w <- nrbm(ordinalRegressionLoss(x,y),LAMBDA=0.001,EPSILON_TOL=0.0001)
w2 <- nrbm(ordinalRegressionLoss(x,y,impl="quadratic"),LAMBDA=0.001,EPSILON_TOL=0.0001)
# -- plot predictions
f <- x %*% w
f2 <- x %*% w2
layout(1:2)
plot(y,f)
plot(f,f2,main="compare predictions of quadratic and loglin implementations")
# -- Compute accuracy
ij <- expand.grid(i=seq(nrow(x)),j=seq(nrow(x)))
n <- tapply(f[ij$i] - f[ij$j]>0,list(y[ij$i],y[ij$j]),sum)
N <- table(y[ij$i],y[ij$j])
print(n/N)
Example output
LowRankQP CONVERGED IN 12 ITERATIONS
Primal Feasibility = 1.0173005e-19
Dual Feasibility = 0.0000000e+00
Complementarity Value = 2.0590219e-12
Duality Gap = 2.0590219e-12
Termination Condition = 2.0590218e-12
1:gap=0.99995 obj=1 reg=0 risk=1 w=[0,0]
LowRankQP CONVERGED IN 11 ITERATIONS
Primal Feasibility = 5.5857624e-17
Dual Feasibility = 1.1102230e-16
Complementarity Value = 2.0651032e-12
Duality Gap = 2.0650753e-12
Termination Condition = 2.0651029e-12
2:gap=0.195788 obj=0.195931 reg=4.97691e-05 risk=0.195881 w=[-0.0301262,0.271402]
LowRankQP CONVERGED IN 12 ITERATIONS
Primal Feasibility = 8.1835214e-18
Dual Feasibility = 2.2204460e-16
Complementarity Value = 3.2324636e-12
Duality Gap = 3.2324595e-12
Termination Condition = 3.2324622e-12
3:gap=0.0948223 obj=0.0952394 reg=0.000143117 risk=0.0950963 w=[-0.0466482,0.459552]
LowRankQP CONVERGED IN 12 ITERATIONS
Primal Feasibility = 2.4607827e-17
Dual Feasibility = 2.2204460e-16
Complementarity Value = 3.7484345e-11
Duality Gap = 3.7484334e-11
Termination Condition = 3.7484305e-11
4:gap=0.0420257 obj=0.043074 reg=0.000417082 risk=0.0426569 w=[0.0155968,0.745712]
LowRankQP CONVERGED IN 12 ITERATIONS
Primal Feasibility = 8.6309063e-19
Dual Feasibility = 1.1102230e-16
Complementarity Value = 2.0598678e-12
Duality Gap = 2.0598677e-12
Termination Condition = 2.0598628e-12
5:gap=0.0142363 obj=0.0166568 reg=0.00104829 risk=0.0156085 w=[-0.256003,1.0919]
LowRankQP CONVERGED IN 12 ITERATIONS
Primal Feasibility = 1.0293895e-18
Dual Feasibility = 1.1102230e-16
Complementarity Value = 6.8236500e-13
Duality Gap = 6.8236499e-13
Termination Condition = 6.8236136e-13
6:gap=0.00408375 obj=0.00941908 reg=0.00242048 risk=0.0069986 w=[-0.449722,1.50098]
LowRankQP CONVERGED IN 11 ITERATIONS
Primal Feasibility = 6.5203168e-17
Dual Feasibility = 4.2188475e-15
Complementarity Value = 3.4600872e-11
Duality Gap = 3.4600863e-11
Termination Condition = 3.4600650e-11
7:gap=0.00301501 obj=0.00941908 reg=0.00242048 risk=0.0069986 w=[-0.449722,1.50098]
LowRankQP CONVERGED IN 12 ITERATIONS
Primal Feasibility = 8.0916782e-19
Dual Feasibility = 0.0000000e+00
Complementarity Value = 2.6610099e-12
Duality Gap = 2.6610098e-12
Termination Condition = 2.6609901e-12
8:gap=0.00195678 obj=0.00941908 reg=0.00242048 risk=0.0069986 w=[-0.449722,1.50098]
LowRankQP CONVERGED IN 12 ITERATIONS
Primal Feasibility = 1.0273815e-17
Dual Feasibility = 2.9976022e-15
Complementarity Value = 8.9925242e-12
Duality Gap = 8.9925232e-12
Termination Condition = 8.9924544e-12
9:gap=0.00123223 obj=0.00899572 reg=0.00403188 risk=0.00496383 w=[-0.414716,2.2088]
LowRankQP CONVERGED IN 13 ITERATIONS
Primal Feasibility = 2.4914498e-17
Dual Feasibility = 4.4408921e-16
Complementarity Value = 4.4243340e-12
Duality Gap = 4.4243301e-12
Termination Condition = 4.4242987e-12
10:gap=0.00101094 obj=0.00899572 reg=0.00403188 risk=0.00496383 w=[-0.414716,2.2088]
LowRankQP CONVERGED IN 13 ITERATIONS
Primal Feasibility = 1.0857923e-16
Dual Feasibility = 1.8096635e-14
Complementarity Value = 6.6332936e-12
Duality Gap = 6.6332622e-12
Termination Condition = 6.6332392e-12
11:gap=0.00037729 obj=0.00858201 reg=0.00333369 risk=0.00524832 w=[-0.611245,1.8206]
LowRankQP CONVERGED IN 15 ITERATIONS
Primal Feasibility = 1.1254578e-16
Dual Feasibility = 0.0000000e+00
Complementarity Value = 6.8655161e-12
Duality Gap = 6.8654921e-12
Termination Condition = 6.8654588e-12
12:gap=0.000240586 obj=0.00858201 reg=0.00333369 risk=0.00524832 w=[-0.611245,1.8206]
LowRankQP CONVERGED IN 14 ITERATIONS
Primal Feasibility = 2.5835074e-15
Dual Feasibility = 6.4392935e-15
Complementarity Value = 1.0903487e-11
Duality Gap = 1.0902893e-11
Termination Condition = 1.0903395e-11
13:gap=0.000215402 obj=0.00858201 reg=0.00333369 risk=0.00524832 w=[-0.611245,1.8206]
LowRankQP CONVERGED IN 14 ITERATIONS
Primal Feasibility = 2.8539943e-18
Dual Feasibility = 8.4376950e-15
Complementarity Value = 1.0178374e-12
Duality Gap = 1.0178372e-12
Termination Condition = 1.0178288e-12
14:gap=0.00012538 obj=0.00858201 reg=0.00333369 risk=0.00524832 w=[-0.611245,1.8206]
LowRankQP CONVERGED IN 13 ITERATIONS
Primal Feasibility = 7.0081487e-17
Dual Feasibility = 7.0610184e-14
Complementarity Value = 5.9873523e-12
Duality Gap = 5.9873411e-12
Termination Condition = 5.9873015e-12
15:gap=7.83959e-05 obj=0.00856749 reg=0.00359877 risk=0.00496872 w=[-0.613904,1.94123]
LowRankQP CONVERGED IN 12 ITERATIONS
Primal Feasibility = 1.0003599e-19
Dual Feasibility = 0.0000000e+00
Complementarity Value = 2.0590219e-12
Duality Gap = 2.0590219e-12
Termination Condition = 2.0590218e-12
1:gap=0.99995 obj=1 reg=0 risk=1 w=[0,0]
LowRankQP CONVERGED IN 11 ITERATIONS
Primal Feasibility = 5.5803453e-17
Dual Feasibility = 1.1102230e-16
Complementarity Value = 2.0651032e-12
Duality Gap = 2.0650753e-12
Termination Condition = 2.0651029e-12
2:gap=0.195788 obj=0.195931 reg=4.97691e-05 risk=0.195881 w=[-0.0301262,0.271402]
LowRankQP CONVERGED IN 12 ITERATIONS
Primal Feasibility = 8.2013176e-18
Dual Feasibility = 2.2204460e-16
Complementarity Value = 3.2324636e-12
Duality Gap = 3.2324595e-12
Termination Condition = 3.2324622e-12
3:gap=0.0948223 obj=0.0952394 reg=0.000143117 risk=0.0950963 w=[-0.0466482,0.459552]
LowRankQP CONVERGED IN 12 ITERATIONS
Primal Feasibility = 2.4573827e-17
Dual Feasibility = 3.3306691e-16
Complementarity Value = 3.7484345e-11
Duality Gap = 3.7484334e-11
Termination Condition = 3.7484305e-11
4:gap=0.0420257 obj=0.043074 reg=0.000417082 risk=0.0426569 w=[0.0155968,0.745712]
LowRankQP CONVERGED IN 12 ITERATIONS
Primal Feasibility = 7.4789301e-19
Dual Feasibility = 1.1102230e-16
Complementarity Value = 2.0598678e-12
Duality Gap = 2.0598677e-12
Termination Condition = 2.0598628e-12
5:gap=0.0142363 obj=0.0166568 reg=0.00104829 risk=0.0156085 w=[-0.256003,1.0919]
LowRankQP CONVERGED IN 12 ITERATIONS
Primal Feasibility = 9.9720218e-19
Dual Feasibility = 2.2204460e-16
Complementarity Value = 6.8236500e-13
Duality Gap = 6.8236499e-13
Termination Condition = 6.8236136e-13
6:gap=0.00408375 obj=0.00941908 reg=0.00242048 risk=0.0069986 w=[-0.449722,1.50098]
LowRankQP CONVERGED IN 11 ITERATIONS
Primal Feasibility = 6.5611727e-17
Dual Feasibility = 3.9968029e-15
Complementarity Value = 3.4600872e-11
Duality Gap = 3.4600863e-11
Termination Condition = 3.4600650e-11
7:gap=0.00301501 obj=0.00941908 reg=0.00242048 risk=0.0069986 w=[-0.449722,1.50098]
LowRankQP CONVERGED IN 12 ITERATIONS
Primal Feasibility = 1.0170599e-18
Dual Feasibility = 1.1102230e-16
Complementarity Value = 2.6610099e-12
Duality Gap = 2.6610098e-12
Termination Condition = 2.6609901e-12
8:gap=0.00195678 obj=0.00941908 reg=0.00242048 risk=0.0069986 w=[-0.449722,1.50098]
LowRankQP CONVERGED IN 12 ITERATIONS
Primal Feasibility = 1.0475479e-17
Dual Feasibility = 3.1086245e-15
Complementarity Value = 8.9925242e-12
Duality Gap = 8.9925232e-12
Termination Condition = 8.9924544e-12
9:gap=0.00123223 obj=0.00899572 reg=0.00403188 risk=0.00496383 w=[-0.414716,2.2088]
LowRankQP CONVERGED IN 13 ITERATIONS
Primal Feasibility = 2.4955261e-17
Dual Feasibility = 4.4408921e-16
Complementarity Value = 4.4243340e-12
Duality Gap = 4.4243300e-12
Termination Condition = 4.4242987e-12
10:gap=0.00101094 obj=0.00899572 reg=0.00403188 risk=0.00496383 w=[-0.414716,2.2088]
LowRankQP CONVERGED IN 13 ITERATIONS
Primal Feasibility = 1.0852316e-16
Dual Feasibility = 1.8096635e-14
Complementarity Value = 6.6332936e-12
Duality Gap = 6.6332622e-12
Termination Condition = 6.6332392e-12
11:gap=0.00037729 obj=0.00858201 reg=0.00333369 risk=0.00524832 w=[-0.611245,1.8206]
LowRankQP CONVERGED IN 15 ITERATIONS
Primal Feasibility = 1.1132028e-16
Dual Feasibility = 1.1102230e-16
Complementarity Value = 6.8655161e-12
Duality Gap = 6.8654921e-12
Termination Condition = 6.8654588e-12
12:gap=0.000240586 obj=0.00858201 reg=0.00333369 risk=0.00524832 w=[-0.611245,1.8206]
LowRankQP CONVERGED IN 14 ITERATIONS
Primal Feasibility = 2.5833831e-15
Dual Feasibility = 6.4392935e-15
Complementarity Value = 1.0903487e-11
Duality Gap = 1.0902893e-11
Termination Condition = 1.0903395e-11
13:gap=0.000215402 obj=0.00858201 reg=0.00333369 risk=0.00524832 w=[-0.611245,1.8206]
LowRankQP CONVERGED IN 14 ITERATIONS
Primal Feasibility = 2.8690552e-18
Dual Feasibility = 8.4376950e-15
Complementarity Value = 1.0178374e-12
Duality Gap = 1.0178372e-12
Termination Condition = 1.0178288e-12
14:gap=0.00012538 obj=0.00858201 reg=0.00333369 risk=0.00524832 w=[-0.611245,1.8206]
LowRankQP CONVERGED IN 13 ITERATIONS
Primal Feasibility = 6.9961993e-17
Dual Feasibility = 7.0721207e-14
Complementarity Value = 5.9873523e-12
Duality Gap = 5.9873411e-12
Termination Condition = 5.9873015e-12
15:gap=7.83959e-05 obj=0.00856749 reg=0.00359877 risk=0.00496872 w=[-0.613904,1.94123]
1 2 3
1 0.4900 0.0000 0.0000
2 1.0000 0.4900 0.0028
3 1.0000 0.9972 0.4896
bmrm documentation built on May 2, 2019, 2:49 p.m.
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Description Usage Arguments Value References See Also Examples
Description
The loss function for ordinal regression
Usage
1 | ordinalRegressionLoss(x, y, C = "0/1", impl = c("loglin", "quadratic"))
|
Arguments
x |
matrix of training instances (one instance by row) |
y |
integer vector of positive values (>=1) representing the training labels for each instance in x |
C |
the cost matrix to use, C[i,j] being the cost for predicting label i instead of label j. |
impl |
either the string "loglin" or "quadratic", that define the implementation to use for the computation of the loss. |
Value
a function taking one argument w and computing the loss value and the gradient at point w
References
Teo et al. Bundle Methods for Regularized Risk Minimization JMLR 2010
See Also
nrbm
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | # -- Load the data
x <- data.matrix(iris[1:4])
y <- as.integer(iris$Species)
# -- Train the model
w <- nrbm(ordinalRegressionLoss(x,y),LAMBDA=0.001,EPSILON_TOL=0.0001)
w2 <- nrbm(ordinalRegressionLoss(x,y,impl="quadratic"),LAMBDA=0.001,EPSILON_TOL=0.0001)
# -- plot predictions
f <- x %*% w
f2 <- x %*% w2
layout(1:2)
plot(y,f)
plot(f,f2,main="compare predictions of quadratic and loglin implementations")
# -- Compute accuracy
ij <- expand.grid(i=seq(nrow(x)),j=seq(nrow(x)))
n <- tapply(f[ij$i] - f[ij$j]>0,list(y[ij$i],y[ij$j]),sum)
N <- table(y[ij$i],y[ij$j])
print(n/N)
|
Example output
LowRankQP CONVERGED IN 12 ITERATIONS
Primal Feasibility = 1.0173005e-19
Dual Feasibility = 0.0000000e+00
Complementarity Value = 2.0590219e-12
Duality Gap = 2.0590219e-12
Termination Condition = 2.0590218e-12
1:gap=0.99995 obj=1 reg=0 risk=1 w=[0,0]
LowRankQP CONVERGED IN 11 ITERATIONS
Primal Feasibility = 5.5857624e-17
Dual Feasibility = 1.1102230e-16
Complementarity Value = 2.0651032e-12
Duality Gap = 2.0650753e-12
Termination Condition = 2.0651029e-12
2:gap=0.195788 obj=0.195931 reg=4.97691e-05 risk=0.195881 w=[-0.0301262,0.271402]
LowRankQP CONVERGED IN 12 ITERATIONS
Primal Feasibility = 8.1835214e-18
Dual Feasibility = 2.2204460e-16
Complementarity Value = 3.2324636e-12
Duality Gap = 3.2324595e-12
Termination Condition = 3.2324622e-12
3:gap=0.0948223 obj=0.0952394 reg=0.000143117 risk=0.0950963 w=[-0.0466482,0.459552]
LowRankQP CONVERGED IN 12 ITERATIONS
Primal Feasibility = 2.4607827e-17
Dual Feasibility = 2.2204460e-16
Complementarity Value = 3.7484345e-11
Duality Gap = 3.7484334e-11
Termination Condition = 3.7484305e-11
4:gap=0.0420257 obj=0.043074 reg=0.000417082 risk=0.0426569 w=[0.0155968,0.745712]
LowRankQP CONVERGED IN 12 ITERATIONS
Primal Feasibility = 8.6309063e-19
Dual Feasibility = 1.1102230e-16
Complementarity Value = 2.0598678e-12
Duality Gap = 2.0598677e-12
Termination Condition = 2.0598628e-12
5:gap=0.0142363 obj=0.0166568 reg=0.00104829 risk=0.0156085 w=[-0.256003,1.0919]
LowRankQP CONVERGED IN 12 ITERATIONS
Primal Feasibility = 1.0293895e-18
Dual Feasibility = 1.1102230e-16
Complementarity Value = 6.8236500e-13
Duality Gap = 6.8236499e-13
Termination Condition = 6.8236136e-13
6:gap=0.00408375 obj=0.00941908 reg=0.00242048 risk=0.0069986 w=[-0.449722,1.50098]
LowRankQP CONVERGED IN 11 ITERATIONS
Primal Feasibility = 6.5203168e-17
Dual Feasibility = 4.2188475e-15
Complementarity Value = 3.4600872e-11
Duality Gap = 3.4600863e-11
Termination Condition = 3.4600650e-11
7:gap=0.00301501 obj=0.00941908 reg=0.00242048 risk=0.0069986 w=[-0.449722,1.50098]
LowRankQP CONVERGED IN 12 ITERATIONS
Primal Feasibility = 8.0916782e-19
Dual Feasibility = 0.0000000e+00
Complementarity Value = 2.6610099e-12
Duality Gap = 2.6610098e-12
Termination Condition = 2.6609901e-12
8:gap=0.00195678 obj=0.00941908 reg=0.00242048 risk=0.0069986 w=[-0.449722,1.50098]
LowRankQP CONVERGED IN 12 ITERATIONS
Primal Feasibility = 1.0273815e-17
Dual Feasibility = 2.9976022e-15
Complementarity Value = 8.9925242e-12
Duality Gap = 8.9925232e-12
Termination Condition = 8.9924544e-12
9:gap=0.00123223 obj=0.00899572 reg=0.00403188 risk=0.00496383 w=[-0.414716,2.2088]
LowRankQP CONVERGED IN 13 ITERATIONS
Primal Feasibility = 2.4914498e-17
Dual Feasibility = 4.4408921e-16
Complementarity Value = 4.4243340e-12
Duality Gap = 4.4243301e-12
Termination Condition = 4.4242987e-12
10:gap=0.00101094 obj=0.00899572 reg=0.00403188 risk=0.00496383 w=[-0.414716,2.2088]
LowRankQP CONVERGED IN 13 ITERATIONS
Primal Feasibility = 1.0857923e-16
Dual Feasibility = 1.8096635e-14
Complementarity Value = 6.6332936e-12
Duality Gap = 6.6332622e-12
Termination Condition = 6.6332392e-12
11:gap=0.00037729 obj=0.00858201 reg=0.00333369 risk=0.00524832 w=[-0.611245,1.8206]
LowRankQP CONVERGED IN 15 ITERATIONS
Primal Feasibility = 1.1254578e-16
Dual Feasibility = 0.0000000e+00
Complementarity Value = 6.8655161e-12
Duality Gap = 6.8654921e-12
Termination Condition = 6.8654588e-12
12:gap=0.000240586 obj=0.00858201 reg=0.00333369 risk=0.00524832 w=[-0.611245,1.8206]
LowRankQP CONVERGED IN 14 ITERATIONS
Primal Feasibility = 2.5835074e-15
Dual Feasibility = 6.4392935e-15
Complementarity Value = 1.0903487e-11
Duality Gap = 1.0902893e-11
Termination Condition = 1.0903395e-11
13:gap=0.000215402 obj=0.00858201 reg=0.00333369 risk=0.00524832 w=[-0.611245,1.8206]
LowRankQP CONVERGED IN 14 ITERATIONS
Primal Feasibility = 2.8539943e-18
Dual Feasibility = 8.4376950e-15
Complementarity Value = 1.0178374e-12
Duality Gap = 1.0178372e-12
Termination Condition = 1.0178288e-12
14:gap=0.00012538 obj=0.00858201 reg=0.00333369 risk=0.00524832 w=[-0.611245,1.8206]
LowRankQP CONVERGED IN 13 ITERATIONS
Primal Feasibility = 7.0081487e-17
Dual Feasibility = 7.0610184e-14
Complementarity Value = 5.9873523e-12
Duality Gap = 5.9873411e-12
Termination Condition = 5.9873015e-12
15:gap=7.83959e-05 obj=0.00856749 reg=0.00359877 risk=0.00496872 w=[-0.613904,1.94123]
LowRankQP CONVERGED IN 12 ITERATIONS
Primal Feasibility = 1.0003599e-19
Dual Feasibility = 0.0000000e+00
Complementarity Value = 2.0590219e-12
Duality Gap = 2.0590219e-12
Termination Condition = 2.0590218e-12
1:gap=0.99995 obj=1 reg=0 risk=1 w=[0,0]
LowRankQP CONVERGED IN 11 ITERATIONS
Primal Feasibility = 5.5803453e-17
Dual Feasibility = 1.1102230e-16
Complementarity Value = 2.0651032e-12
Duality Gap = 2.0650753e-12
Termination Condition = 2.0651029e-12
2:gap=0.195788 obj=0.195931 reg=4.97691e-05 risk=0.195881 w=[-0.0301262,0.271402]
LowRankQP CONVERGED IN 12 ITERATIONS
Primal Feasibility = 8.2013176e-18
Dual Feasibility = 2.2204460e-16
Complementarity Value = 3.2324636e-12
Duality Gap = 3.2324595e-12
Termination Condition = 3.2324622e-12
3:gap=0.0948223 obj=0.0952394 reg=0.000143117 risk=0.0950963 w=[-0.0466482,0.459552]
LowRankQP CONVERGED IN 12 ITERATIONS
Primal Feasibility = 2.4573827e-17
Dual Feasibility = 3.3306691e-16
Complementarity Value = 3.7484345e-11
Duality Gap = 3.7484334e-11
Termination Condition = 3.7484305e-11
4:gap=0.0420257 obj=0.043074 reg=0.000417082 risk=0.0426569 w=[0.0155968,0.745712]
LowRankQP CONVERGED IN 12 ITERATIONS
Primal Feasibility = 7.4789301e-19
Dual Feasibility = 1.1102230e-16
Complementarity Value = 2.0598678e-12
Duality Gap = 2.0598677e-12
Termination Condition = 2.0598628e-12
5:gap=0.0142363 obj=0.0166568 reg=0.00104829 risk=0.0156085 w=[-0.256003,1.0919]
LowRankQP CONVERGED IN 12 ITERATIONS
Primal Feasibility = 9.9720218e-19
Dual Feasibility = 2.2204460e-16
Complementarity Value = 6.8236500e-13
Duality Gap = 6.8236499e-13
Termination Condition = 6.8236136e-13
6:gap=0.00408375 obj=0.00941908 reg=0.00242048 risk=0.0069986 w=[-0.449722,1.50098]
LowRankQP CONVERGED IN 11 ITERATIONS
Primal Feasibility = 6.5611727e-17
Dual Feasibility = 3.9968029e-15
Complementarity Value = 3.4600872e-11
Duality Gap = 3.4600863e-11
Termination Condition = 3.4600650e-11
7:gap=0.00301501 obj=0.00941908 reg=0.00242048 risk=0.0069986 w=[-0.449722,1.50098]
LowRankQP CONVERGED IN 12 ITERATIONS
Primal Feasibility = 1.0170599e-18
Dual Feasibility = 1.1102230e-16
Complementarity Value = 2.6610099e-12
Duality Gap = 2.6610098e-12
Termination Condition = 2.6609901e-12
8:gap=0.00195678 obj=0.00941908 reg=0.00242048 risk=0.0069986 w=[-0.449722,1.50098]
LowRankQP CONVERGED IN 12 ITERATIONS
Primal Feasibility = 1.0475479e-17
Dual Feasibility = 3.1086245e-15
Complementarity Value = 8.9925242e-12
Duality Gap = 8.9925232e-12
Termination Condition = 8.9924544e-12
9:gap=0.00123223 obj=0.00899572 reg=0.00403188 risk=0.00496383 w=[-0.414716,2.2088]
LowRankQP CONVERGED IN 13 ITERATIONS
Primal Feasibility = 2.4955261e-17
Dual Feasibility = 4.4408921e-16
Complementarity Value = 4.4243340e-12
Duality Gap = 4.4243300e-12
Termination Condition = 4.4242987e-12
10:gap=0.00101094 obj=0.00899572 reg=0.00403188 risk=0.00496383 w=[-0.414716,2.2088]
LowRankQP CONVERGED IN 13 ITERATIONS
Primal Feasibility = 1.0852316e-16
Dual Feasibility = 1.8096635e-14
Complementarity Value = 6.6332936e-12
Duality Gap = 6.6332622e-12
Termination Condition = 6.6332392e-12
11:gap=0.00037729 obj=0.00858201 reg=0.00333369 risk=0.00524832 w=[-0.611245,1.8206]
LowRankQP CONVERGED IN 15 ITERATIONS
Primal Feasibility = 1.1132028e-16
Dual Feasibility = 1.1102230e-16
Complementarity Value = 6.8655161e-12
Duality Gap = 6.8654921e-12
Termination Condition = 6.8654588e-12
12:gap=0.000240586 obj=0.00858201 reg=0.00333369 risk=0.00524832 w=[-0.611245,1.8206]
LowRankQP CONVERGED IN 14 ITERATIONS
Primal Feasibility = 2.5833831e-15
Dual Feasibility = 6.4392935e-15
Complementarity Value = 1.0903487e-11
Duality Gap = 1.0902893e-11
Termination Condition = 1.0903395e-11
13:gap=0.000215402 obj=0.00858201 reg=0.00333369 risk=0.00524832 w=[-0.611245,1.8206]
LowRankQP CONVERGED IN 14 ITERATIONS
Primal Feasibility = 2.8690552e-18
Dual Feasibility = 8.4376950e-15
Complementarity Value = 1.0178374e-12
Duality Gap = 1.0178372e-12
Termination Condition = 1.0178288e-12
14:gap=0.00012538 obj=0.00858201 reg=0.00333369 risk=0.00524832 w=[-0.611245,1.8206]
LowRankQP CONVERGED IN 13 ITERATIONS
Primal Feasibility = 6.9961993e-17
Dual Feasibility = 7.0721207e-14
Complementarity Value = 5.9873523e-12
Duality Gap = 5.9873411e-12
Termination Condition = 5.9873015e-12
15:gap=7.83959e-05 obj=0.00856749 reg=0.00359877 risk=0.00496872 w=[-0.613904,1.94123]
1 2 3
1 0.4900 0.0000 0.0000
2 1.0000 0.4900 0.0028
3 1.0000 0.9972 0.4896
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