# lineSearch: A curvilinear search on the Stiefel manifold (Wen and Yin... In rstiefel: Random Orthonormal Matrix Generation and Optimization on the Stiefel Manifold

## Description

A curvilinear search on the Stiefel manifold (Wen and Yin 2013, Algo 1)

## Usage

 `1` ```lineSearch(F, dF, X, rho1, rho2, tauStart, maxIters = 20) ```

## Arguments

 `F` A function V(n, p) -> `R^1` `dF` A function V(n, p) -> `R^1` `X` an n x p semi-orthogonal matrix (starting point) `rho1` Parameter for Armijo condition. Between 0 and 1 and usually small, e.g < 0.1 `rho2` Parameter for Wolfe condition Between 0 and 1 usually large, > 0.9 `tauStart` Initial step size `maxIters` Maximum number of iterations

## Value

A list containing: Y, the semi-orthogonal matrix satisfying the Armijo-Wolfe conditions and tau: the stepsize satisfying these conditions

Alexander Franks

## References

(Wen and Yin, 2013)

## Examples

 ```1 2 3 4 5 6 7``` ```N <- 10 P <- 2 M <- diag(10:1) F <- function(V) { - sum(diag(t(V) %*% M %*% V)) } dF <- function(V) { - 2*M %*% V } X <- rustiefel(N, P) res <- lineSearch(F, dF, X, rho1=0.1, rho2=0.9, tauStart=1) ```

rstiefel documentation built on June 12, 2018, 5:19 p.m.