TRES (version 0.1.0)

OptimballGBB1D: Estimate the envelope subspace (Feasi 1D)

Description

The 1D algorithm to estimate the envelope subspace with specified dimension based on Wen and Yin (2013).

Usage

OptimballGBB1D(M, U, u, opts=NULL)

Arguments

M

M matrix in the envelope objective function. A \(p\)-by-\(p\) positive semi-definite matrix.

U

U matrix in the envelope objective function. A \(p\)-by-\(p\) positive semi-definite matrix.

u

Dimension of the envelope. An integer between 0 and \(p\).

opts

Option structure with fields: "record = 0" -- no print out. "mxitr" -- max number of iterations. "xtol" -- stop control for \(||X_k - X_{k-1}||\). "gtol" -- stop control for the projected gradient. "ftol" -- stop control for \(\frac{|F_k - F_{k-1}|}{(1+|F_{k-1}|)}\) usually with max{xtol, gtol} > ftol.

The default values are: "xtol"=1e-08; "gtol"=1e-08; "ftol"=1e-12; "mxitr"=500.

Value

Ghat

The orthogonal basis of the envelope subspace with each column represent the sequential direction. For example, the 1st column is the most informative direction.

Details

Estimate M-envelope contains span(U) where M > 0 and is symmetric. The dimension of the envelope is u.

References

Wen, Z., & Yin, W. (2013). A feasible method for optimization with orthogonality constraints. Mathematical Programming, 142(1-2), 397-434.

Examples

# NOT RUN {
##simulate two matrices M and U with an envelope structure#
data <- MenvU_sim(n=200, p=20, u=5, Omega=NULL, Omega0=NULL, Phi=NULL)
Mhat <- data$Mhat
Uhat <- data$Uhat
G <- data$Gamma

Ghat_1D <- OptimballGBB1D(Mhat, Uhat, u=5)
subspace(Ghat_1D, G)
# }