lineSearchBB: A curvilinear search on the Stiefel manifold with BB steps...

In pdhoff/rstiefel: Random Orthonormal Matrix Generation and Optimization on the Stiefel Manifold

Description

A curvilinear search on the Stiefel manifold with BB steps (Wen and Yin 2013, Algo 2) This is based on the line search algorithm described in (Zhang and Hager, 2004)

Usage

lineSearchBB(F, X, Xprev, G_x, G_xprev, rho, C, maxIters = 20)

Arguments

F	A function V(n, p) -> R
X	an n x p semi-orthogonal matrix (the current )
Xprev	an n x p semi-orthogonal matrix (the previous)
G_x	an n x p matrix with (G_x)_ij = dF(X)/dX_ij
G_xprev	an n x p matrix with (G_xprev)_ij = dF(X_prev)/dX_prev_ij
rho	Convergence parameter, usually small (e.g. 0.1)
C	C_t+1 = (etaQ_t + F(X_t+1))/Q_t+1 See section 3.2 in Wen and Yin, 2013
maxIters	Maximum number of iterations

Value

A list containing Y: a semi-orthogonal matrix Ytau which satisfies convergence criteria (Eqn 29 in Wen & Yin '13), and tau: the stepsize satisfying these criteria

Author(s)

Alexander Franks

References

(Wen and Yin, 2013) and (Zhang and Hager, 2004)

Examples

N <- 10
P <- 2
M <- diag(10:1)
F <- function(V) { - sum(diag(t(V) %*% M %*% V)) }
dF <- function(V) { - 2*M %*% V }
Xprev <- rustiefel(N, P)
G_xprev <- dF(Xprev)
X <- rustiefel(N, P)
G_x <- dF(X)
Xprev <- dF(X)
res <- lineSearchBB(F, X, Xprev, G_x, G_xprev, rho=0.1, C=F(X))

pdhoff/rstiefel documentation built on June 16, 2021, 5:36 p.m.