prox.boundednondecreasing: Proximal operator for the set of bounded non-decreasing...

In jpvert/apg: Optimization with accelerated proximal gradient

Description

Computes the proximal operator of the bounded non-decreasing vectors, i.e.,

prox(x) = argmin_u || u - x ||^2 such that u_1 ≤ ... ≤ u_n and ||u|| ≤ M

This is simply the projection of $x$ onto the set of non-decreasing vectors, obtained by isotonic regression, followed by projection onto the Euclidean ball of radius $M$.

Usage

prox.boundednondecreasing(x, t = 0, opts = list())

Arguments

x	The input vector
opts	Optional list of parameters, which can include: maxnorm : the bound on the Euclidean norm of the non-decreasing vector (default 1).

Value

The projection of x onto the set of nondecreasing vectors with norm bounded by maxnorm.

Examples

a <- rnorm(20)+1
plot(a)
lines(prox.boundednondecreasing(a), col=2)
lines(prox.boundednondecreasing(a, opts=list(maxnorm=10)), col=3)

jpvert/apg documentation built on May 19, 2019, 11:51 p.m.