The validity of the ``pool-adjacent-violator'' algorithm
The purpose of this paper is to show that if G is a positive definite symmetric real matrix, the solution to minimize \((g-x)'G(g-x)\) subject to \(x'A\geq 0\) can be determined through the pool-adjacent-violator (PAV) algorithm if and only if the restrictions cone, \(\hat A,\) is acute. We also show that such a solution can be determined in one step if and only if \(\hat A\) is right-angled. In the problem of isotonic regression \(\hat A\) is acute.
scientific article; zbMATH DE number 4030711