OptManiMulitBallGBB

n by k matrix such that \(X'X = I\)

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

opts

Objective function and its gradient:
 <code>fun(X, data1, data2)</code>
 <code>data1, data2</code> are additional data.

Additional input for <code>fun</code>, Calling syntax:
 <code>OptManiMulitBallGBB(X0, fun, opts, data1, data2)</code>.

Line search algorithm for optimization on Stiefel manifold based on Wen and Yin (2013). Used in 1D-algorithm for estimating the envelope subspace.

Provides three estimators for tensor response regression (TRR) and tensor predictor regression (TPR) models with tensor envelope structure. The three types of estimation approaches are generic and can be applied to any envelope estimation problems. The full Grassmannian (FG) optimization is often associated with likelihood-based estimation but requires heavy computation and good initialization; the one-directional optimization approaches (1D and ECD algorithms) are faster, stable and does not require carefully chosen initial values; the SIMPLS-type is motivated by the partial least squares regression and is computationally the least expensive. For details of TRR, see Li L, Zhang X (2017) <doi:10.1080/01621459.2016.1193022>. For details of TPR, see Zhang X, Li L (2017) <doi:10.1080/00401706.2016.1272495>. For details of 1D algorithm, see Cook RD, Zhang X (2016) <doi:10.1080/10618600.2015.1029577>. For details of ECD algorithm, see Cook RD, Zhang X (2018) <doi:10.5705/ss.202016.0037>.

OptManiMulitBallGBB: Line search algorithm for optimization on manifold

Description

Usage

Arguments

Value

References