OptStiefelGBB: Optimization on Stiefel manifold (GBB)

In kusakehan/TEReg: An R package for tensor envelope regression with tensor response and tensor predictor

Description

Curvilinear search algorithm for optimization on Stiefel manifold based on Wen and Yin (2013). Used for estimating the envelope subspace.

Usage

OptStiefelGBB(X, opts=NULL, fun, ...)

Arguments

X	n by k matrix such that X'X = I
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.
fun	Objective function and its gradient: fun(X, data1, data2) data1, data2 are addtional data.
...	Additional input for fun, Calling syntax: OptStiefelGBB(X0, fun, opts, data1, data2).

Value

X	Solution
Out	Output information, inclusde estimation error, function value, iteration times etc.

References

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

Examples

fun <- function(X,  A) {
      G = -2*(A %*% X)
      F = sum(diag(t(X) %*% A %*% X))
      return(list(F = F, G = G))
}
n = 1000; k = 6;
A = matrix(rnorm(n^2), n, n); A = t(A) %*% A

opts=c()
opts$record = 0;
opts$mxitr  = 1000;
opts$xtol = 1e-5;
opts$gtol = 1e-5;
opts$ftol = 1e-8;

X0 = matrix(rnorm(n*k), n, k);
X0 = qr.Q(qr(X0));

eva <- OptStiefelGBB(X0, opts, fun, A)
X <- eva$X
out <- eva$out
out$fval = -2*out$fval;

kusakehan/TEReg documentation built on May 30, 2019, 7:17 a.m.