8 problems

Let $S$ be defined by an arbitrary number of ball constraints, and let ${\cal D}:=\operatorname{cone}\{(xx^\top,x):~x\in S\}\subseteq {\mathbb{S}}^n_+\oplus {\mathbb{R}}^n$ be the…

Let $\text{\sc Beta}$ denote the convex relaxation of the ball-constrained nonconvex quadratic program defined in the paper, with matrix variable $W$ and vectors $\ell_1,\ell_2$ as…

Optimal-row conjecture. The row used for the optimal partition should be of a form similar to

Strict-decrease partitioning conjecture. If $l_k<l_k^{(i)}$, $u_k^{(i)}<u_k$, $l\le l^{(i)}$, and $u^{(i)}\le u$ for every $i\in\{1,2,\dots,p\}$, then the $k$th coordinate of the…

Consider instances of best subset selection for which a mixed-integer optimization solver does not prove optimality within the allotted computation time, and compare their optimali…

The experiments compare several convex relaxations and solvers for non-binary discrete tomography, including the more efficient implementation $\textbf{CBC\_CB}$ and branch-and-bou…

Consider the $\ell_0$-based sparse regression problem and an exact reformulation of such $\ell_0$-regularized problems as optimization problems involving convex functions in Boolea…

Let a third-order tensor have a t-SVD with f-diagonal tensor $\boldsymbol{\mathscr{S}}$, and define its tensor-tubal-rank as the number of nonzero diagonal tubes…