PSM_solver: Solve given problem in parametric simplex method
In PRIMAL: Parametric Simplex Method for Sparse Learning

Description Usage Arguments Value See Also Examples

Solve given problem in parametric simplex method

1 2	PSM_solver(A, b, b_bar, c, c_bar, B_init = NULL, max_it = 50, lambda_threshold = 0.01)

`A`	`A` is an `n` by `d` data matrix
`b`	`b` is a length `n` response vector
`b_bar`	`b_bar` is a length `n` vector time to parameter in constraints.
`c`	`c` is a length `d` vector in target function.
`c_bar`	`c_bar` is a length `d` vector time to parameter in target function
`B_init`	`B_init` is the index of initial basic colume.
`max_it`	This is the number of the maximum path length one would like to achieve. The default length is `50`.
`lambda_threshold`	The parametric simplex method will stop when the calculated parameter is smaller than lambda. The default value is `0.01`.

An object with S3 class "primal" is returned:

`data`	The `n` by `d` data matrix from the input
`response`	The length `n` response vector from the input
`beta`	A matrix of regression estimates whose columns correspond to regularization parameters for parametric simplex method.
`beta0`	A vector of regression estimates whose index correspond to regularization parameters for parametric simplex method.
`df`	The degree of freecom (number of nonzero coefficients) along the solution path.
`value`	The sequence of optimal value of the object function corresponded to the sequence of lambda.
`iterN`	The number of iteration in the program.
`lambda`	The sequence of regularization parameters `lambda` obtained in the program.
`type`	The type of the problem, such as `Dantzig` and `SparseSVM`.

primal-package

## This example show how to use PSM_solver() to solve dantzig problem.
## Generate the design matrix and coefficient vector
n = 100 # sample number
d = 250 # sample dimension
c = 0.5 # correlation parameter
s = 20  # support size of coefficient
set.seed(1024)
X = scale(matrix(rnorm(n*d),n,d)+c*rnorm(n))/sqrt(n-1)*sqrt(n)
beta = c(rnorm(s), rep(0, d-s))
## Generate response using Gaussian noise, and solve the solution path
noise = rnorm(n)
Y = X%*%beta + noise
## Define parameters for dantzig problem
XtX = t(X)%*%X
A = cbind(cbind(rbind(XtX,-XtX),-rbind(XtX,-XtX)),diag(rep(1,2*d)))
b = rbind(t(X)%*%Y,-t(X)%*%Y)
c = c(rep(-1,2*d),rep(0,2*d))
c_bar = rep(0,4*d)
b_bar = rep(1,2*d)
B_init = seq(2*d,4*d-1)
## Dantzig selection solved with parametric simplex method
fit.dantzig = PSM_solver(A, b, b_bar, c, c_bar, B_init, max_it = 50, lambda_threshold = 0.01)
###lambdas used
print(fit.dantzig$lambda)
## number of nonzero coefficients for each lambda
print(fit.dantzig$df)
## Visualize the solution path
plot(fit.dantzig)