17 problems

For any $(v_0,v)\in\mathbb{R}^{n+1}$, let $\text{E-CG}(v_0,v)$ denote the corresponding Eigen-CG inequality, and let BH inequalities denote the Boros–Hammer inequalities. Nonnegati…

A cutting-plane learning problem considers candidate cuts evaluated by a gap-closed score, with attention restricted to cuts that cut off the current fractional solution. Gap-close…

Conjecture on the speedup difference. These two features are the reasons for the smaller speedup in the exact setting.

The separation problem asks whether, for a given sparse separable bilinear program and point, a violated lifted bilinear cover inequality can be found. NP-hardness conjecture. We c…

De Farias et al.'s separation-complexity conjecture. The separation problems for both of these inequalities are $\mathcal{NP}$-complete.

Non-facetness conjecture. The derived inequalities are not facet-defining for $\operatorname{lmc}(C)$.

The face dimension of a cut is the dimension of the face it induces in the feasible region of a mixed-integer linear program; empirically, face dimensions are often concentrated ne…

Let $k\in\mathbb{N}$ be fixed. For a rational polyhedron $P\subseteq\mathbb{R}^n$, define the $k$-dimensional projection closure by … where $\mathcal{L}_k$ is the family of $k$-dim…

Let $k\geq 3$ and $n\geq k$. For a rational polyhedron $P\subseteq\mathbb{R}^n$, let $\mathcal{H}_k(P)$ be its $k$-halfspace closure, and let … where $\mathcal{L}_k$ is the family…

Let $k\in\mathbb{N}$ be fixed. For a rational polyhedron $P$, define the $k$-halfspace closure by … where $Q_I$ denotes the integer hull of $Q$. Polyhedrality conjecture for the…

A Tseitin formula is indexed by a constant-degree graph $G=(V,E)$ and parities $l_v\in\{0,1\}$ satisfying … Its variables are $\mathbf{x}\in\{0,1\}^E$, with the assignment satisfyi…

Let the full-dimensional integer hull depth be the depth measure introduced in the paper, and let Theorem denote its lower bound, while Lemma and Theorem provide the relevant upper…

The experiments compare several formulations for quadratic optimization with indicator variables, including formulations with and without cuts, and consider instances whose size is…

Generalized minor inequality sufficiency conjecture. Generalized minor inequalities, together with boolean facets and the rank constraint, are sufficient for describing

Let $\boldsymbol{\nu}=(\lambda_1,\ldots,\lambda_m,\nu)$ be an augmented vector of the form specified in the source, and consider the multiplicative and additive optimization proble…

NP-hardness conjecture. This optimization problem is also $NP$-hard. It is the additive strategy for choosing an iterated Chvátal--Gomory cut with small norm and positive rounding…

NP-hardness conjecture. This optimization problem is $NP$-hard. The problem arises in selecting an integer multiplier that simultaneously keeps the multiplier vector small and prod…