6 problems

Lasso active-set constraints. The Lasso choice must satisfy ${\mathcal A}_1\subseteq {\mathcal A}$ and ${\mathcal A}\subseteq {\mathcal A}_{10}$; moreover, $w_{\mathcal A}$ cannot…

Let $u^2$ and $u^2_h$ denote the infinite-dimensional and discrete second iterates, respectively, and let $abla (u^2-u^2h)$ be measured in $L^2( Omega)$. Let $lambda^2h$ be the d…

The paper considers interior-point methods for bound-constrained nonlinear optimization problems with bounded noise, relaxing only the Armijo line-search condition while retaining…

Extension conjecture. The algorithm can be readily extended to deal with significantly more general problems, either by appropriately extending its associated theory or by adjustin…

Active-set extension conjecture. The algorithm can be readily extended to deal with general nonlinear convex objectives, or discretizations of stochastic two-stage problems.

The problems considered involve noisy data, with $m=10\,000$ constraints and the number of variables $n$ ranging from 10 to 500. Let $M_Q$ denote the matrix whose ill-conditioning…