OptManiMulitBallGBB: Line search algorithm for optimization on manifold

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

Description

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

Usage

OptManiMulitBallGBB(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.
fun	Objective function and its gradient: fun(X, data1, data2) data1, data2 are addtional data.
...	Additional input for fun, Calling syntax: OptManiMulitBallGBB(X0, fun, opts, data1, data2).

Value

X	Solution.
g	Gradient of X.
Out	Output information, include 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.

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