Description Usage Arguments Details Value
View source: R/opt_alpha_only.R
penalized optimization of the constrained linearized perspective function
1 2 |
y |
length n vector |
z |
n \times J matrix |
a0 |
length J vector |
eps |
length J vector, default to be rep(0.1/J, J) |
reltol |
relative tolerence for Newton step, between 0 to 1, default to be 10^{-3}. For each inner loop, we optimize f_0 + ρ \times \mathrm{pen} for a fixed ρ, we stop when the Newton decrement f(x) - inf_y \hat{f}(y) ≤q f(x)* \mathrm{reltol}, where \hat{f} is the second-order approximation of f at x |
relerr |
relerr stop when within (1+relerr) of minimum variance, default to be 10^{-3}, between 0 to 1. |
rho0 |
initial value for ρ, default to be 1 |
maxin |
maximum number of inner iterations |
maxout |
maximum number of outer iterations |
To minimize ∑_i \frac{y_i^2}{z_i^Tα} over α subject to α_j > ε_j for j = 1, \cdots, J and ∑_{j=1}^J α_j < 1,
Instead we minimize ∑_i \frac{y_i^2}{z_i^Tα} + ρ \times \mathrm{pen} for a decreasing sequence of ρ
where \mathrm{pen} = -( ∑_{j = 1}^J( \log(α_j-ε_j) ) + \log(1-∑_{j = 1}^J α_j) )
starting values are α = a0 and can be missing.
The optimization stops when within (1+relerr) of minimum variance.
a list of
input y
input z
optimized alpha
value of rho
value of the objective function
value of rho*pen when returned
number of outer loops
relative error
sum of optimized alpha
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.